https://cirpwiki.info/api.php?action=feedcontributions&user=U4hcsdaw&feedformat=atomCIRPwiki - User contributions [en]2024-03-29T15:22:26ZUser contributionsMediaWiki 1.39.2https://cirpwiki.info/index.php?title=Grays_Harbor&diff=10622Grays Harbor2014-04-23T17:07:27Z<p>U4hcsdaw: </p>
<hr />
<div>= Purpose =<br />
<br />
The CMS performance in simulating the hydrodynamics and wave<br />
transformation at a relatively large and complex inlet and estuary at<br />
Grays Harbor, WA is analyzed using field measurements of water levels<br />
and current velocities. The specific model features to be tested are<br />
the wave-flow coupling, user-defined water level boundary condition,<br />
and wetting and drying.<br />
<br />
= Field Study =<br />
<br />
Grays Harbor is located on the southwest Washington coast about<br />
45 miles north of the Columbia River. The estuary has a wetted surface<br />
area of approximately 91 square miles at mean higher high water and 28<br />
squares miles at mean lower low water. The main input of fresh water<br />
is from the Chehalis River. The 3-mile wide entrance has two<br />
convergent rock jetties which extend from spit points, as shown in<br />
Figure 1. In 1999 and 2001, the USACE conducted several field<br />
experiments at Grays Harbor as part of a navigation study to better<br />
understand the sediment transport and functionality of the northern<br />
jetty (Osborne et al. 2002). During 1999, measurements of water<br />
levels, current velocities, and suspended sediment were collected at<br />
seven locations (black dots in Figure 1). Here in the current<br />
velocity data collected September to October of 1999 are used for<br />
validation. For further details on the field experiment the reader is<br />
referred to Osborne et al. (2002). For water levels, NOAA tide gauge<br />
stations were used due to their distal location from the inlet<br />
entrance (red dots in Figure 1).<br />
<br />
= Model Setup =<br />
<br />
The computational grid consisted of 67,000 cells and had a non-uniform<br />
spacing from 28 to 200 m. The model domain is shown in Figure 1. Both<br />
the wave and flow models used the same grid. The spectral waves from<br />
the NOAA buoy 46029 were input at the model boundaries every<br />
3 hr. Wind from the same buoy was included in the wave model. The<br />
hydrodynamic, sediment transport and morphologic time steps were set<br />
to 15 min. A spatially constant Manning’s roughness coefficient was<br />
calibrated as 0.018 s/m1/3 using water level measurements and was the<br />
only parameter calibrated. The hydrodynamic model was forced with<br />
water level measurements taken at Station 0. The 27-day period from<br />
September 14 to October 15 of 1999 was calculated with CMS. The model<br />
setup is summarized in Table 1. For further details on the model<br />
setup and results see Wu et al. (2010). The 27-day simulation took<br />
approximately 7 hr on a single 2.67GHz processor.<br />
<br />
[[File:Grays_Harbor.png |thumb|right|400px|Figure 1. CMS computational domain for the Grays Harbor, WA test case.]]<br />
<br />
{| border="1"<br />
|+ Table 1. CMS model settings for the Grays Harbor test case.<br />
!Parameter !!Value<br />
|-<br />
|Time step ||15 min<br />
|-<br />
|Simulation duration ||27 days<br />
|-<br />
|Ramp period ||24 hr<br />
|-<br />
|Manning’s coefficient ||0.018 1/m1/3<br />
|-<br />
|Steering interval ||3 hr<br />
|}<br />
<br />
<br />
= Results and Discussion =<br />
<br />
Figures 2-3 compare the computed and measured water levels and<br />
current velocities at selected stations. The agreement between<br />
calculated and measured water levels is generally good as demonstrated<br />
by the goodness-of-fit statistics presented in Table 2. There is a<br />
slight over prediction of the water level at Stations 3 and 4 during<br />
low tide and may be associated with bathymetric error or an over<br />
estimation of bottom roughness which prevents the water from ebbing<br />
during low tide. It is possible that the results may be improved by<br />
using a spatially variable bottom roughness based on the bottom and is<br />
planned for future work. Different time steps between 5-30 min were<br />
tested and the differences were negligible. The only areas which show<br />
significant differences are those with extensive wetting and<br />
drying. However, these areas contain a relatively small tidal prism<br />
and do not significantly impact the dynamics near the inlet<br />
entrance. It is interesting to note from the water levels (see<br />
Figure 2) that the hydrodynamics took approximately 250 hr to<br />
eliminate the effect of the initial condition. This suggests that the<br />
model needs a spin-up period of approximately 11 days possibly due to<br />
the presence of resonance inside bay which takes time for the model to<br />
build up.<br />
<br />
[[File:Grays_Harbor_Tide_Levels.png |thumb|right|400px|Figure 2. Measured and calculated tide levels at Grays Harbor, WA. MTL = Mean Tide Level. Elapsed times are with respect to September 14, 1999.]]<br />
<br />
{| border="1"<br />
|+ Table 2. Goodness-of-fit statistics for the water levels at Grays Harbor, WA.<br />
!Statistic !!Sta1 !!Sta2 !!Sta3 !!Sta4<br />
|-<br />
|NRMSE, % ||2.61 ||2.87 ||7.17 ||5.14<br />
|-<br />
|NMAE, % ||2.03 ||2.41 ||5.38 ||3.78<br />
|-<br />
|R2 ||0.990 ||0.991 ||0.968 ||0.979<br />
|-<br />
|Bias, m ||-0.017 ||-0.049 ||-0.132 ||-0.106<br />
|}<br />
<br />
Measured (estimated from vertical velocity profile) and calculated<br />
depth-averaged current velocities are compared along the current<br />
principle axis because it represents the major component of the<br />
current velocity variance. Peak ebb and flood current velocities<br />
ranges from approximately 1-1.5 m/s. In general, the model predicts<br />
well the amplitude and phase of the principle current velocities<br />
well. Normalized errors for the principle current velocities are less<br />
than 10% indicating a good model performance (see Table 3).<br />
<br />
[[File:Grays_Harbor_Velocities.png |thumb|right|400px|Figure 3. Measured and calculated principle current velocities at Grays Harbor, WA. Elapsed times are with respect to September 14, 1999. ]]<br />
<br />
{| border="1"<br />
|+ Table 3. Principle current velocity goodness-of-fit statistics for Grays Harbor, WA.<br />
!Statistic !!Sta 1 !!Sta 2 !!Sta 3 !!Sta 4 !!Sta 5 !!Sta 6<br />
|-<br />
|NRMSE, % ||10.09 ||6.74 ||8.15 ||6.13 ||6.14 ||7.33<br />
|-<br />
|NMAE, % ||8.53 ||5.11 ||5.93 ||5.04 ||4.74 ||6.08<br />
|-<br />
|R2 ||0.916 ||0.970 ||0.979 ||0.981 ||0.974 ||0.9702<br />
|-<br />
|Bias, m/s ||0.053 ||-0.041 ||0.123 ||-0.027 ||0.0244 ||0.0816<br />
|}<br />
<br />
As stated in Chapter 1, validation is the process of determining<br />
whether the governing equations represent the physics of the specific<br />
problem studied. When a single time-series measurement is used for<br />
calibration, the comparison between measured and computed values<br />
cannot be considered validation. However, if a model is reasonably<br />
calibrated using several measurement locations and variables such as<br />
water levels, velocities, fluxes, etc, than it arguable that the<br />
calibration results also serve to demonstrate the model validity since<br />
it would be highly improbable if not impossible to obtain a good<br />
agreement at several locations for all variables without the model<br />
accurately representing the physics of the problem being studied. A<br />
reasonable calibration is one which uses few calibration parameters<br />
and uses parameters within physically meaningful or previously<br />
reported limits. Rigorous validation requires that the calibration<br />
dataset be separate and independent of the calibration<br />
dataset. However, in coastal hydrodynamics, this can be difficult due<br />
to limited data and the fact that different study periods may have<br />
significantly different geometries due to changing bathymetry and<br />
physics (tidal vs wind- and wave-induced currents, stratified vs<br />
non-stratified, time varying bed composition and friction, exposed vs<br />
unexposed hard bottom, etc.).<br />
<br />
<br />
= Conclusions and Recommendations =<br />
<br />
The CMS performance in simulating tidal hydrodynamics at a coastal<br />
inlet in the presence of wave and wind was tested for Grays Harbor, WA<br />
using field measurements of water levels and current velocities. Water<br />
levels and depth-averaged principle current velocities were compared<br />
at several stations and four goodness-of-fit statistics were used to<br />
assess the model performance. In general, the model results agree well<br />
with measurements. Although the model ramp period was only 24 hr, the<br />
time period for the model hydrodynamics to reach dynamic equilibrium<br />
in the bay (i.e. to fully spin-up) was approximately 250 hr. The model<br />
results demonstrate that it is reasonable to use large time steps on<br />
the order of 15 min for similar tidal inlet hydrodynamic<br />
studies. Using such a large time step will however, reduce the<br />
accuracy of the wetting and drying. If this is considered to be an<br />
important aspect of the study, than a smaller time step may be more<br />
adequate.<br />
<br />
<br />
= References =<br />
* Osborne, P.D., Herricks, D.B., and Kraus, N.C., and Parry, R. M. (2002). “Wide-Area Measurements of Sediment Transport at a Large Inlet, Grays Harbor, WA,” Proceedings 28th Coastal Engineering Conference, World Scientific, 3053-3064.<br />
* Wu, W., Sánchez, A., and Zhang, M. (2011a). "An Implicit 2-D Depth-Averaged Finite-Volume Model of Flow and Sediment Transport in Coastal Waters", ICCE 2010.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10621Li2014-04-23T17:05:10Z<p>U4hcsdaw: </p>
<hr />
<div>= Purpose =<br />
<br />
Application of CMS to the Gironde Estuary demonstrates specification<br />
of the flow boundary condition within an estuary, with validation<br />
measurements of water level and current speed spaced along the axis of<br />
the estuary.<br />
<br />
<br />
<br />
= Field Study =<br />
<br />
The Gironde Estuary is located in southwestern France. It receives<br />
runoff from the Garonne and the Dordogne Rivers and opens up to the<br />
Atlantic Ocean, as shown in Figure 1. The water-surface width varies<br />
from 2 to 14 km, and the flow depth in the navigation channel ranges<br />
from 6 to 30 m. The estuary is partially mixed and macrotidal, with a<br />
12 hr and 25 min tidal lunar period and a tidal amplitude of 1.5 to<br />
5 m at the mouth (Li et al. 1994).<br />
<br />
[[File:Gironde_Estuary.png |thumb|right|400px|Figure 1. Sketch of the Gironde Estuary, France (from Wu and Wang 2004).]]<br />
<br />
<br />
= Model Setup =<br />
<br />
The implicit CMS was applied to this test case, with the simulation<br />
domain extending 80 km starting from the mouth at the Atlantic Ocean<br />
to the Garonne and Dordogne Rivers. The bed topography was provided on<br />
a uniform mesh, with a size of 250 × 125 m for each cell. The grid has<br />
approximately 16,000 active cells. Because the domain is relatively<br />
simple, a uniform mesh was used. The data measured from May 19 to 25,<br />
1975 were used to validate the model for water level and current<br />
speed. The computational time step was set to 30 min. At the estuary<br />
mouth, the tidal elevation was given by the recorded time series at<br />
the station “Pointe de Grave” (see Figure 1). At the two upstream<br />
ends, the flow discharges of the Garonne River and the Dordogne River<br />
were specified according to the measured data at La Réole and<br />
Pessac. The Manning’s roughness coefficient was set to<br />
0.018 s/m1/3. Figure 2 shows the computational grid and observation<br />
stations. The Coriolis force is included using the f-plane<br />
approximation. Winds were not included in the simulation. The 100-hr<br />
simulation took approximately 12 min to run on a 2.67 GHz processor.<br />
<br />
[[File:Gironde_Estuary_Computational_Grid.png |thumb|right|400px|Figure 2. Computational grid and observation stations for the Gironde Estuary Test Case.]]<br />
<br />
<br />
The inland boundaries along the Dordogne and Garonne rivers were<br />
assigned as flux boundary conditions according to the data from La<br />
Réole and Pessac, and the inflow discharges were set to 387 and<br />
846 m3/s, respectively. The initial condition was specified as still<br />
water in the whole domain. A 1-hr ramp period was used at the start<br />
the simulation. Table 1 summarizes the setup parameters for CMS.<br />
<br />
{| border="1"<br />
|+ Table 1. CMS-Flow setup parameters for the Gironde Estuary test case.<br />
!Parameter !!Value<br />
|-<br />
|Solution scheme ||Implicit <br />
|-<br />
|Simulation duration ||100 hr <br />
|-<br />
|Ramp period duration ||1 hr <br />
|-<br />
|Time step ||6 min <br />
|-<br />
|Manning’s n coefficient ||0.018 s/m1/3 <br />
|-<br />
|Latitude ||45.5°<br />
|}<br />
<br />
= Results and Discussion =<br />
<br />
The flow fields in flood and ebb tides are shown in Figure 3. The ebb<br />
flow is characterized by a funnel effect at the entrance (mouth or<br />
inlet) caused by the narrowing of the estuary in this region. The<br />
increase in velocity is likely to be the cause of the channel<br />
deepening in this region as shown by the depth contours (see<br />
Figure 2). The flood tide is also characterized by a funnel effect<br />
near Ile Verte which also seems to cause some deepening of the estuary<br />
to the south of the island.<br />
<br />
[[File:Gironde_Currents.png |thumb|right|400px|Figure 3. Examples of ebb (top) and flood (bottom) tidal currents and water surface elevations in the Gironde Estuary.]]<br />
<br />
Figure 4 compares the measured and simulated water levels at five<br />
stations within the Gironde Estuary (stations shown in Figure 2). In<br />
general, the results show good agreement with the measured data both<br />
in amplitude and phase. Table 2 summarizes the goodness–of-fit<br />
statistics for water level. NRMSE and NMAE values for the water levels<br />
range from 5-7%.<br />
<br />
[[File:Gironde_Water_Levels.png |thumb|right|400px|Figure 4. Comparison of measured and calculated water levels at five stations in the Gironde Estuary (stations shown in Figure 2).]]<br />
<br />
{| border="1"<br />
|+ Table 2. Water level goodness-of-fit statistics* for the Gironde Estuary test case.<br />
!Statistic !!Richard !!Lamena !!Pauillac !!Ile Verte !!La Reuille<br />
|-<br />
|NRMSE, % ||5.10 ||7.02 ||6.74 ||6.40 ||6.63<br />
|-<br />
|NMAE, % ||4.33 ||6.21 ||5.63 ||4.34 ||5.08<br />
|-<br />
|<math>R^2</math> ||0.982 ||0.956 ||0.951 ||0.962 ||0.972<br />
|-<br />
|Bias, m ||0.094 ||0.128 ||0.043 ||-0.060 ||-0.0252<br />
|}<br />
<br />
Figure 5 shows the comparison of the measured and simulated flow<br />
velocities at several stations (stations shown in Figure 2). The<br />
velocities were measured 1 m below the water surface and 1 m above the<br />
river bed, respectively. In this figure, positive current velocities<br />
correspond to flood tides and negative velocities to ebb tides. The<br />
current measurements at both elevations are relatively similar for all<br />
stations except Richard and Lamena. This might be due to baroclinic<br />
circulation produced by wind, fresh water intrusion, or other factors<br />
near these two stations.<br />
<br />
Some of the differences in water surface elevations and current<br />
velocities may be due to inaccuracies in the boundary conditions. The<br />
boundary conditions at the estuary entrance was obtained from a nearby<br />
station and therefore a slight phase lag of about 45 min was<br />
subtracted from calculated water surface elevations in order to match<br />
the measured time series. However, since the boundary condition used<br />
was not measured exactly at the location of the boundary, some error<br />
in phase lag may be expected from this approximation.<br />
<br />
Another probable source of error is the bottom roughness coefficient,<br />
which was assumed to be constant. Other field experiments show that<br />
the bottom roughness in an estuary can vary significantly due to<br />
changes in bed forms and grain sizes within the estuary. Although the<br />
CMS has the capability to use a spatially variable bottom roughness<br />
coefficient, there were no data available in this case. The agreement<br />
between measured and calculated current speeds is summarized in<br />
Table 3. NRMSE and NMAE in current speed range from 7-21%. Comparable<br />
results were obtained by Wu and Wang (2004) using a similar<br />
depth-averaged flow model.<br />
<br />
[[File:Gironde_Current_Speed.png |thumb|right|400px|Figure 5. Measured and calculated current speed in the Gironde Estuary (stations shown in Figure 2) ]]<br />
<br />
{| border="1"<br />
|+ Table 3. Current speed goodness of fit statistics for the Gironde Estuary test case.<br />
!Statistic !!Richard !!PK68 !!Lamena !!Pauillac-1 !!Pauillac-2 !!Blaye<br />
|-<br />
|NRMSE, % ||10.70 ||7.27 ||8.81 ||15.89 ||20.73 ||14.98<br />
|-<br />
|NMAE, % ||9.15 ||5.71 ||6.93 ||13.67 ||17.05 ||13.17<br />
|-<br />
|R2 ||0.911 ||0.957 ||0.968 ||0.856 ||0.680 ||0.804<br />
|-<br />
|Bias, m/s ||0.070 ||-0.057 ||0.062 ||0.022 ||-0.031 ||0.095<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
CMS calculations of tidal flow in a large estuary were compared to<br />
measured water level and current speed. Calculations agreed with<br />
measurements with errors ranging from 5-7% for water level and 7-21%<br />
for currents. The boundary condition used in the model was not<br />
measured exactly at the location of the boundary, and therefore the<br />
calculations incurred some error in phase lag of water surface<br />
elevation and in current velocities. This application demonstrates<br />
the accuracy of CMS within a macrotidal estuarine environment, for<br />
measurements distributed along the channel. It is recommended that the<br />
bottom roughness be estimated based on the bottom type (sandy, rocky<br />
outcrops, vegetation, etc.), and then adjusted (calibrated) based on<br />
field measurements of water levels and currents. When developing a new<br />
model setup and grid for engineering applications, it is useful to<br />
start simple as far as grid size and model forcing, and slow increase<br />
the model complexity, only as needed until satisfactory results are<br />
obtained for the purpose of the project. This iterative process has<br />
the added benefit of providing insights on the importance of physical<br />
processes and model sensitivity to setup parameters and grid geometry.<br />
<br />
<br />
= References =<br />
* Li, Z.H., Nguyen, K.D., Brun-Cottan, J.C. and Martin, J.M., (1994). “Numerical simulation of the turbidity maximum transport in the Gironde Estuary (France)” Oceanologica Acta, 17(5), 479–500.<br />
* Wu, W., and Wang, S.S.Y. (2004). “Depth-averaged 2-D calculation of tidal flow, salinity and cohesive sediment transport in estuaries.” International Journal of Sediment Research, 19(3), 172-190.<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Grays_Harbor&diff=10620Grays Harbor2014-04-23T17:01:57Z<p>U4hcsdaw: Created page with "= Purpose = The CMS performance in simulating the hydrodynamics and wave transformation at a relatively large and complex inlet and estuary at Grays Harbor, WA is analyzed us..."</p>
<hr />
<div>= Purpose =<br />
<br />
The CMS performance in simulating the hydrodynamics and wave<br />
transformation at a relatively large and complex inlet and estuary at<br />
Grays Harbor, WA is analyzed using field measurements of water levels<br />
and current velocities. The specific model features to be tested are<br />
the wave-flow coupling, user-defined water level boundary condition,<br />
and wetting and drying.<br />
<br />
= Field Study =<br />
<br />
Grays Harbor is located on the southwest Washington coast about<br />
45 miles north of the Columbia River. The estuary has a wetted surface<br />
area of approximately 91 square miles at mean higher high water and 28<br />
squares miles at mean lower low water. The main input of fresh water<br />
is from the Chehalis River. The 3-mile wide entrance has two<br />
convergent rock jetties which extend from spit points, as shown in<br />
Figure 1. In 1999 and 2001, the USACE conducted several field<br />
experiments at Grays Harbor as part of a navigation study to better<br />
understand the sediment transport and functionality of the northern<br />
jetty (Osborne et al. 2002). During 1999, measurements of water<br />
levels, current velocities, and suspended sediment were collected at<br />
seven locations (black dots in Figure 1). Here in the current<br />
velocity data collected September to October of 1999 are used for<br />
validation. For further details on the field experiment the reader is<br />
referred to Osborne et al. (2002). For water levels, NOAA tide gauge<br />
stations were used due to their distal location from the inlet<br />
entrance (red dots in Figure 1).<br />
<br />
= Model Setup =<br />
<br />
The computational grid consisted of 67,000 cells and had a non-uniform<br />
spacing from 28 to 200 m. The model domain is shown in Figure 1. Both<br />
the wave and flow models used the same grid. The spectral waves from<br />
the NOAA buoy 46029 were input at the model boundaries every<br />
3 hr. Wind from the same buoy was included in the wave model. The<br />
hydrodynamic, sediment transport and morphologic time steps were set<br />
to 15 min. A spatially constant Manning’s roughness coefficient was<br />
calibrated as 0.018 s/m1/3 using water level measurements and was the<br />
only parameter calibrated. The hydrodynamic model was forced with<br />
water level measurements taken at Station 0. The 27-day period from<br />
September 14 to October 15 of 1999 was calculated with CMS. The model<br />
setup is summarized in Table 1. For further details on the model<br />
setup and results see Wu et al. (2010). The 27-day simulation took<br />
approximately 7 hr on a single 2.67GHz processor.<br />
<br />
[[File:Grays_Harbor.png |thumb|right|400px|Figure 1. CMS computational domain for the Grays Harbor, WA test case.]]<br />
<br />
{| border="1"<br />
|+ Table 1. CMS model settings for the Grays Harbor test case.<br />
!Parameter !!Value<br />
|-<br />
|Time step ||15 min<br />
|-<br />
|Simulation duration ||27 days<br />
|-<br />
|Ramp period ||24 hr<br />
|-<br />
|Manning’s coefficient ||0.018 1/m1/3<br />
|-<br />
|Steering interval ||3 hr<br />
|}<br />
<br />
<br />
= Results and Discussion =<br />
<br />
Figures 2-3 compare the computed and measured water levels and<br />
current velocities at selected stations. The agreement between<br />
calculated and measured water levels is generally good as demonstrated<br />
by the goodness-of-fit statistics presented in Table 2. There is a<br />
slight over prediction of the water level at Stations 3 and 4 during<br />
low tide and may be associated with bathymetric error or an over<br />
estimation of bottom roughness which prevents the water from ebbing<br />
during low tide. It is possible that the results may be improved by<br />
using a spatially variable bottom roughness based on the bottom and is<br />
planned for future work. Different time steps between 5-30 min were<br />
tested and the differences were negligible. The only areas which show<br />
significant differences are those with extensive wetting and<br />
drying. However, these areas contain a relatively small tidal prism<br />
and do not significantly impact the dynamics near the inlet<br />
entrance. It is interesting to note from the water levels (see<br />
Figure 2) that the hydrodynamics took approximately 250 hr to<br />
eliminate the effect of the initial condition. This suggests that the<br />
model needs a spin-up period of approximately 11 days possibly due to<br />
the presence of resonance inside bay which takes time for the model to<br />
build up.<br />
<br />
[[File:Grays_Harbor_Tide_Levels.png |thumb|right|400px|Figure 2. Measured and calculated tide levels at Grays Harbor, WA. MTL = Mean Tide Level. Elapsed times are with respect to September 14, 1999.]]<br />
<br />
{| border="1"<br />
|+ Table 2. Goodness-of-fit statistics for the water levels at Grays Harbor, WA.<br />
!Statistic !!Sta1 !!Sta2 !!Sta3 !!Sta4<br />
|-<br />
|NRMSE, % ||2.61 ||2.87 ||7.17 ||5.14<br />
|-<br />
|NMAE, % ||2.03 ||2.41 ||5.38 ||3.78<br />
|-<br />
|R2 ||0.990 ||0.991 ||0.968 ||0.979<br />
|-<br />
|Bias, m ||-0.017 ||-0.049 ||-0.132 ||-0.106<br />
|}<br />
<br />
Measured (estimated from vertical velocity profile) and calculated<br />
depth-averaged current velocities are compared along the current<br />
principle axis because it represents the major component of the<br />
current velocity variance. Peak ebb and flood current velocities<br />
ranges from approximately 1-1.5 m/s. In general, the model predicts<br />
well the amplitude and phase of the principle current velocities<br />
well. Normalized errors for the principle current velocities are less<br />
than 10% indicating a good model performance (see Table 3).<br />
<br />
[[File:Grays_Harbor_Velocities.png |thumb|right|400px|Figure 3. Measured and calculated principle current velocities at Grays Harbor, WA. Elapsed times are with respect to September 14, 1999. ]]<br />
<br />
{| border="1"<br />
|+ Table 3. Principle current velocity goodness-of-fit statistics for Grays Harbor, WA.<br />
!Statistic !!Sta 1 !!Sta 2 !!Sta 3 !!Sta 4 !!Sta 5 !!Sta 6<br />
|-<br />
|NRMSE, % ||10.09 ||6.74 ||8.15 ||6.13 ||6.14 ||7.33<br />
|-<br />
|NMAE, % ||8.53 ||5.11 ||5.93 ||5.04 ||4.74 ||6.08<br />
|-<br />
|R2 ||0.916 ||0.970 ||0.979 ||0.981 ||0.974 ||0.9702<br />
|-<br />
|Bias, m/s ||0.053 ||-0.041 ||0.123 ||-0.027 ||0.0244 ||0.0816<br />
|}<br />
<br />
As stated in Chapter 1, validation is the process of determining<br />
whether the governing equations represent the physics of the specific<br />
problem studied. When a single time-series measurement is used for<br />
calibration, the comparison between measured and computed values<br />
cannot be considered validation. However, if a model is reasonably<br />
calibrated using several measurement locations and variables such as<br />
water levels, velocities, fluxes, etc, than it arguable that the<br />
calibration results also serve to demonstrate the model validity since<br />
it would be highly improbable if not impossible to obtain a good<br />
agreement at several locations for all variables without the model<br />
accurately representing the physics of the problem being studied. A<br />
reasonable calibration is one which uses few calibration parameters<br />
and uses parameters within physically meaningful or previously<br />
reported limits. Rigorous validation requires that the calibration<br />
dataset be separate and independent of the calibration<br />
dataset. However, in coastal hydrodynamics, this can be difficult due<br />
to limited data and the fact that different study periods may have<br />
significantly different geometries due to changing bathymetry and<br />
physics (tidal vs wind- and wave-induced currents, stratified vs<br />
non-stratified, time varying bed composition and friction, exposed vs<br />
unexposed hard bottom, etc.).<br />
<br />
<br />
= Conclusions and Recommendations =<br />
<br />
The CMS performance in simulating tidal hydrodynamics at a coastal<br />
inlet in the presence of wave and wind was tested for Grays Harbor, WA<br />
using field measurements of water levels and current velocities. Water<br />
levels and depth-averaged principle current velocities were compared<br />
at several stations and four goodness-of-fit statistics were used to<br />
assess the model performance. In general, the model results agree well<br />
with measurements. Although the model ramp period was only 24 hr, the<br />
time period for the model hydrodynamics to reach dynamic equilibrium<br />
in the bay (i.e. to fully spin-up) was approximately 250 hr. The model<br />
results demonstrate that it is reasonable to use large time steps on<br />
the order of 15 min for similar tidal inlet hydrodynamic<br />
studies. Using such a large time step will however, reduce the<br />
accuracy of the wetting and drying. If this is considered to be an<br />
important aspect of the study, than a smaller time step may be more<br />
adequate.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Grays_Harbor.png&diff=10619File:Grays Harbor.png2014-04-23T17:00:26Z<p>U4hcsdaw: MsUpload</p>
<hr />
<div>MsUpload</div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Grays_Harbor_Velocities.png&diff=10618File:Grays Harbor Velocities.png2014-04-23T17:00:25Z<p>U4hcsdaw: MsUpload</p>
<hr />
<div>MsUpload</div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Grays_Harbor_Tide_Levels.png&diff=10617File:Grays Harbor Tide Levels.png2014-04-23T17:00:24Z<p>U4hcsdaw: MsUpload</p>
<hr />
<div>MsUpload</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Test_Cases&diff=10616Test Cases2014-04-23T16:59:34Z<p>U4hcsdaw: /* Current-Wave Interaction */</p>
<hr />
<div><big><br />
__NOTOC__<br />
<font color=red>'''UNDER CONSTRUCTION'''</font><br />
== Hydrodynamics ==<br />
'''Analytical'''<br />
# [[Long wave propagation | Analytical Solution of long wave propagation in a Quarter Annulus (Lynch 1978)]]<br />
# [[Wind Setup | Analytical Solution for Wind Setup]]<br />
# [[Flow over a bump | Analytical Solution for Flow over a Bump]]<br />
# [[Long-wave Runup | Analytical Solution for Long-wave Runup over a Planar Slope (Carrier et al. 2003)]]<br />
# [[Circular Basin | Analytical Solution for Wind-driven Flow in a Circular Basin (Dupont 2001)]]<br />
# [[Standing wave in a rectangular basin | Analytical Solution for a Standing Wave in a Rectangular Basin (Lamb 1945)]]<br />
<br />
'''Laboratory'''<br />
# [[Spure Dike | Rectangular Flume with a Spure Dike (Rajaratnam and Nwachukwu 1983) ]]<br />
# [[Sudden Expansion | Rectangular Flume with Sudden Expansion (Xie 1996)]]<br />
# [[Nested Idealized Inlet]]<br />
# [[Planar Beach | Planar sloping beach with oblique incident regular wave]]<br />
# [[Idealized jettied inlet | Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves]]<br />
<br />
== Sediment Transport ==<br />
=== Channel Infilling ===<br />
# [[Channel infilling under steady currents | Channel infilling by currents (Galappatti and Vreugdenhil 1985)]]<br />
# [[Channel infilling under waves parallel to steady currents | Channel infilling by currents and waves parallel to flow (van Rijn 1986)]]<br />
# [[Channel infilling under waves perpendicular to steady currents | Channel infilling by currents and waves perpendicular to flow (van Rijn and Havinga 1993)]]<br />
<br />
=== Erosion Tests ===<br />
# [[Clear water jet | Clear water jet (Thuc 1991)]]<br />
<br />
=== Morphology Change ===<br />
# [[Morphology Change Validation of Shark River Inlet | Model Application to Shark River Inlet]]<br />
# [[Model Application to St. Augustine Inlet |Morphology Change Validation to St. Augustine Inlet]]<br />
<br />
=== Nonuniform Sediments ===<br />
# [[Deposition of Nonuniform Sediments | Downstream Fining of Nonuniform Sediments (Seal et al. 1995)]]<br />
<br />
== Salinity ==<br />
<br />
# [[Salinity | Salinity Transport Modeling at White Ditch Area, LA]]<br />
# [[Salinity Calculations in the Jupiter Inlet - Loxahatchee River System, FL]]<br />
<br />
== Structures==<br />
# [[Rubble Mound Tests | Rubble Mound Verification and Sensitivity]]<br />
# [[Weir Tests | Weir Application and Validation at Bonnet Carre Spillway, MS]]<br />
# [[Culvert Tests | Culvert Application and Validation at White Ditch, MS ]]<br />
# [[Structure | Evaluation of breakwaters and sedimentation at Dana Point Harbor, CA]]<br />
<br />
== Waves ==<br />
# [[Rosati, James | Mississippi Coastal Improvement Program (MsCIP) Validation to Wave Measurements ]]<br />
# [[Lab Wave Validation Case 1 | CMS-Wave 2008 - Lab Case 1 ]]<br />
# [[Lab Wave Validation Case 2 | CMS-Wave 2008 - Lab Case 2 ]]<br />
# [[Lab Wave Validation Case 3 | CMS-Wave 2008 - Lab Case 3 ]]<br />
# [[Field Experiment Wave Validation Case 1 | CMS-Wave 2008 - Field Case 1 ]]<br />
# [[Field Experiment Wave Validation Case 2 | CMS-Wave 2008 - Field Case 2 ]]<br />
# [[Field Experiment Wave Validation Case 3 | CMS-Wave 2008 - Field Case 3 ]]<br />
<br />
== Current-Wave Interaction ==<br />
# [[Visser | Regular Waves Breaking on a Planar Beach (Visser 1991)]]<br />
# [[LSTF | Random Waves Breaking on a Natural Beach (LSTF 2007)]]<br />
# [[Kuriyama_Ozaki | Random Waves Breaking on Barred Beach (Kuriyama and Ozaki 1993)]]<br />
# [[DELILAH | Random Waves Breaking on Barred Beach (Smith et al. 1993)]]<br />
# [[SEABERGH | Regular Waves on an Idealized Inlet (Seabergh et al. 2005)]]<br />
# [[Li | Gironde Estuary, France (Li et al. 1994).]]<br />
# [[Grays Harbor | Grays Harbor, Washington ]]<br />
# [[Tri-Cusp Beach | Regular Waves Breaking on a Planar Beach with Three Cusps (Borthwick and Foote 2002)]]<br />
<br />
----<br />
<br />
[[CMS#Documentation_Portal | Documentation Portal]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10615Li2014-04-23T16:57:53Z<p>U4hcsdaw: /* Results and Discussion */</p>
<hr />
<div>= Purpose =<br />
<br />
Application of CMS to the Gironde Estuary demonstrates specification<br />
of the flow boundary condition within an estuary, with validation<br />
measurements of water level and current speed spaced along the axis of<br />
the estuary.<br />
<br />
<br />
<br />
= Field Study =<br />
<br />
The Gironde Estuary is located in southwestern France. It receives<br />
runoff from the Garonne and the Dordogne Rivers and opens up to the<br />
Atlantic Ocean, as shown in Figure 1. The water-surface width varies<br />
from 2 to 14 km, and the flow depth in the navigation channel ranges<br />
from 6 to 30 m. The estuary is partially mixed and macrotidal, with a<br />
12 hr and 25 min tidal lunar period and a tidal amplitude of 1.5 to<br />
5 m at the mouth (Li et al. 1994).<br />
<br />
[[File:Gironde_Estuary.png |thumb|right|400px|Figure 1. Sketch of the Gironde Estuary, France (from Wu and Wang 2004).]]<br />
<br />
<br />
= Model Setup =<br />
<br />
The implicit CMS was applied to this test case, with the simulation<br />
domain extending 80 km starting from the mouth at the Atlantic Ocean<br />
to the Garonne and Dordogne Rivers. The bed topography was provided on<br />
a uniform mesh, with a size of 250 × 125 m for each cell. The grid has<br />
approximately 16,000 active cells. Because the domain is relatively<br />
simple, a uniform mesh was used. The data measured from May 19 to 25,<br />
1975 were used to validate the model for water level and current<br />
speed. The computational time step was set to 30 min. At the estuary<br />
mouth, the tidal elevation was given by the recorded time series at<br />
the station “Pointe de Grave” (see Figure 1). At the two upstream<br />
ends, the flow discharges of the Garonne River and the Dordogne River<br />
were specified according to the measured data at La Réole and<br />
Pessac. The Manning’s roughness coefficient was set to<br />
0.018 s/m1/3. Figure 2 shows the computational grid and observation<br />
stations. The Coriolis force is included using the f-plane<br />
approximation. Winds were not included in the simulation. The 100-hr<br />
simulation took approximately 12 min to run on a 2.67 GHz processor.<br />
<br />
[[File:Gironde_Estuary_Computational_Grid.png |thumb|right|400px|Figure 2. Computational grid and observation stations for the Gironde Estuary Test Case.]]<br />
<br />
<br />
The inland boundaries along the Dordogne and Garonne rivers were<br />
assigned as flux boundary conditions according to the data from La<br />
Réole and Pessac, and the inflow discharges were set to 387 and<br />
846 m3/s, respectively. The initial condition was specified as still<br />
water in the whole domain. A 1-hr ramp period was used at the start<br />
the simulation. Table 1 summarizes the setup parameters for CMS.<br />
<br />
{| border="1"<br />
|+ Table 1. CMS-Flow setup parameters for the Gironde Estuary test case.<br />
!Parameter !!Value<br />
|-<br />
|Solution scheme ||Implicit <br />
|-<br />
|Simulation duration ||100 hr <br />
|-<br />
|Ramp period duration ||1 hr <br />
|-<br />
|Time step ||6 min <br />
|-<br />
|Manning’s n coefficient ||0.018 s/m1/3 <br />
|-<br />
|Latitude ||45.5°<br />
|}<br />
<br />
= Results and Discussion =<br />
<br />
The flow fields in flood and ebb tides are shown in Figure 3. The ebb<br />
flow is characterized by a funnel effect at the entrance (mouth or<br />
inlet) caused by the narrowing of the estuary in this region. The<br />
increase in velocity is likely to be the cause of the channel<br />
deepening in this region as shown by the depth contours (see<br />
Figure 2). The flood tide is also characterized by a funnel effect<br />
near Ile Verte which also seems to cause some deepening of the estuary<br />
to the south of the island.<br />
<br />
[[File:Gironde_Currents.png |thumb|right|400px|Figure 3. Examples of ebb (top) and flood (bottom) tidal currents and water surface elevations in the Gironde Estuary.]]<br />
<br />
Figure 4 compares the measured and simulated water levels at five<br />
stations within the Gironde Estuary (stations shown in Figure 2). In<br />
general, the results show good agreement with the measured data both<br />
in amplitude and phase. Table 2 summarizes the goodness–of-fit<br />
statistics for water level. NRMSE and NMAE values for the water levels<br />
range from 5-7%.<br />
<br />
[[File:Gironde_Water_Levels.png |thumb|right|400px|Figure 4. Comparison of measured and calculated water levels at five stations in the Gironde Estuary (stations shown in Figure 2).]]<br />
<br />
{| border="1"<br />
|+ Table 2. Water level goodness-of-fit statistics* for the Gironde Estuary test case.<br />
!Statistic !!Richard !!Lamena !!Pauillac !!Ile Verte !!La Reuille<br />
|-<br />
|NRMSE, % ||5.10 ||7.02 ||6.74 ||6.40 ||6.63<br />
|-<br />
|NMAE, % ||4.33 ||6.21 ||5.63 ||4.34 ||5.08<br />
|-<br />
|<math>R^2</math> ||0.982 ||0.956 ||0.951 ||0.962 ||0.972<br />
|-<br />
|Bias, m ||0.094 ||0.128 ||0.043 ||-0.060 ||-0.0252<br />
|}<br />
<br />
Figure 5 shows the comparison of the measured and simulated flow<br />
velocities at several stations (stations shown in Figure 2). The<br />
velocities were measured 1 m below the water surface and 1 m above the<br />
river bed, respectively. In this figure, positive current velocities<br />
correspond to flood tides and negative velocities to ebb tides. The<br />
current measurements at both elevations are relatively similar for all<br />
stations except Richard and Lamena. This might be due to baroclinic<br />
circulation produced by wind, fresh water intrusion, or other factors<br />
near these two stations.<br />
<br />
Some of the differences in water surface elevations and current<br />
velocities may be due to inaccuracies in the boundary conditions. The<br />
boundary conditions at the estuary entrance was obtained from a nearby<br />
station and therefore a slight phase lag of about 45 min was<br />
subtracted from calculated water surface elevations in order to match<br />
the measured time series. However, since the boundary condition used<br />
was not measured exactly at the location of the boundary, some error<br />
in phase lag may be expected from this approximation.<br />
<br />
Another probable source of error is the bottom roughness coefficient,<br />
which was assumed to be constant. Other field experiments show that<br />
the bottom roughness in an estuary can vary significantly due to<br />
changes in bed forms and grain sizes within the estuary. Although the<br />
CMS has the capability to use a spatially variable bottom roughness<br />
coefficient, there were no data available in this case. The agreement<br />
between measured and calculated current speeds is summarized in<br />
Table 3. NRMSE and NMAE in current speed range from 7-21%. Comparable<br />
results were obtained by Wu and Wang (2004) using a similar<br />
depth-averaged flow model.<br />
<br />
[[File:Gironde_Current_Speed.png |thumb|right|400px|Figure 5. Measured and calculated current speed in the Gironde Estuary (stations shown in Figure 2) ]]<br />
<br />
{| border="1"<br />
|+ Table 3. Current speed goodness of fit statistics for the Gironde Estuary test case.<br />
!Statistic !!Richard !!PK68 !!Lamena !!Pauillac-1 !!Pauillac-2 !!Blaye<br />
|-<br />
|NRMSE, % ||10.70 ||7.27 ||8.81 ||15.89 ||20.73 ||14.98<br />
|-<br />
|NMAE, % ||9.15 ||5.71 ||6.93 ||13.67 ||17.05 ||13.17<br />
|-<br />
|R2 ||0.911 ||0.957 ||0.968 ||0.856 ||0.680 ||0.804<br />
|-<br />
|Bias, m/s ||0.070 ||-0.057 ||0.062 ||0.022 ||-0.031 ||0.095<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
CMS calculations of tidal flow in a large estuary were compared to<br />
measured water level and current speed. Calculations agreed with<br />
measurements with errors ranging from 5-7% for water level and 7-21%<br />
for currents. The boundary condition used in the model was not<br />
measured exactly at the location of the boundary, and therefore the<br />
calculations incurred some error in phase lag of water surface<br />
elevation and in current velocities. This application demonstrates<br />
the accuracy of CMS within a macrotidal estuarine environment, for<br />
measurements distributed along the channel. It is recommended that the<br />
bottom roughness be estimated based on the bottom type (sandy, rocky<br />
outcrops, vegetation, etc.), and then adjusted (calibrated) based on<br />
field measurements of water levels and currents. When developing a new<br />
model setup and grid for engineering applications, it is useful to<br />
start simple as far as grid size and model forcing, and slow increase<br />
the model complexity, only as needed until satisfactory results are<br />
obtained for the purpose of the project. This iterative process has<br />
the added benefit of providing insights on the importance of physical<br />
processes and model sensitivity to setup parameters and grid geometry.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Gironde_Current_Speed.png&diff=10614File:Gironde Current Speed.png2014-04-23T16:57:06Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Gironde_Water_Levels.png&diff=10613File:Gironde Water Levels.png2014-04-23T16:56:39Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Gironde_Currents.png&diff=10612File:Gironde Currents.png2014-04-23T16:56:10Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Gironde_Estuary_Computational_Grid.png&diff=10611File:Gironde Estuary Computational Grid.png2014-04-23T16:55:46Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Gironde_Estuary.png&diff=10610File:Gironde Estuary.png2014-04-23T16:54:35Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10609Li2014-04-23T16:53:56Z<p>U4hcsdaw: </p>
<hr />
<div>= Purpose =<br />
<br />
Application of CMS to the Gironde Estuary demonstrates specification<br />
of the flow boundary condition within an estuary, with validation<br />
measurements of water level and current speed spaced along the axis of<br />
the estuary.<br />
<br />
<br />
<br />
= Field Study =<br />
<br />
The Gironde Estuary is located in southwestern France. It receives<br />
runoff from the Garonne and the Dordogne Rivers and opens up to the<br />
Atlantic Ocean, as shown in Figure 1. The water-surface width varies<br />
from 2 to 14 km, and the flow depth in the navigation channel ranges<br />
from 6 to 30 m. The estuary is partially mixed and macrotidal, with a<br />
12 hr and 25 min tidal lunar period and a tidal amplitude of 1.5 to<br />
5 m at the mouth (Li et al. 1994).<br />
<br />
[[File:Gironde_Estuary.png |thumb|right|400px|Figure 1. Sketch of the Gironde Estuary, France (from Wu and Wang 2004).]]<br />
<br />
<br />
= Model Setup =<br />
<br />
The implicit CMS was applied to this test case, with the simulation<br />
domain extending 80 km starting from the mouth at the Atlantic Ocean<br />
to the Garonne and Dordogne Rivers. The bed topography was provided on<br />
a uniform mesh, with a size of 250 × 125 m for each cell. The grid has<br />
approximately 16,000 active cells. Because the domain is relatively<br />
simple, a uniform mesh was used. The data measured from May 19 to 25,<br />
1975 were used to validate the model for water level and current<br />
speed. The computational time step was set to 30 min. At the estuary<br />
mouth, the tidal elevation was given by the recorded time series at<br />
the station “Pointe de Grave” (see Figure 1). At the two upstream<br />
ends, the flow discharges of the Garonne River and the Dordogne River<br />
were specified according to the measured data at La Réole and<br />
Pessac. The Manning’s roughness coefficient was set to<br />
0.018 s/m1/3. Figure 2 shows the computational grid and observation<br />
stations. The Coriolis force is included using the f-plane<br />
approximation. Winds were not included in the simulation. The 100-hr<br />
simulation took approximately 12 min to run on a 2.67 GHz processor.<br />
<br />
[[File:Gironde_Estuary_Computational_Grid.png |thumb|right|400px|Figure 2. Computational grid and observation stations for the Gironde Estuary Test Case.]]<br />
<br />
<br />
The inland boundaries along the Dordogne and Garonne rivers were<br />
assigned as flux boundary conditions according to the data from La<br />
Réole and Pessac, and the inflow discharges were set to 387 and<br />
846 m3/s, respectively. The initial condition was specified as still<br />
water in the whole domain. A 1-hr ramp period was used at the start<br />
the simulation. Table 1 summarizes the setup parameters for CMS.<br />
<br />
{| border="1"<br />
|+ Table 1. CMS-Flow setup parameters for the Gironde Estuary test case.<br />
!Parameter !!Value<br />
|-<br />
|Solution scheme ||Implicit <br />
|-<br />
|Simulation duration ||100 hr <br />
|-<br />
|Ramp period duration ||1 hr <br />
|-<br />
|Time step ||6 min <br />
|-<br />
|Manning’s n coefficient ||0.018 s/m1/3 <br />
|-<br />
|Latitude ||45.5°<br />
|}<br />
<br />
= Results and Discussion =<br />
<br />
The flow fields in flood and ebb tides are shown in Figure 3. The ebb<br />
flow is characterized by a funnel effect at the entrance (mouth or<br />
inlet) caused by the narrowing of the estuary in this region. The<br />
increase in velocity is likely to be the cause of the channel<br />
deepening in this region as shown by the depth contours (see<br />
Figure 2). The flood tide is also characterized by a funnel effect<br />
near Ile Verte which also seems to cause some deepening of the estuary<br />
to the south of the island.<br />
<br />
[[File:Gironde_Currents.png |thumb|right|400px|Figure 3. Examples of ebb (top) and flood (bottom) tidal currents and water surface elevations in the Gironde Estuary.]]<br />
<br />
Figure 4 compares the measured and simulated water levels at five<br />
stations within the Gironde Estuary (stations shown in Figure 2). In<br />
general, the results show good agreement with the measured data both<br />
in amplitude and phase. Table 2 summarizes the goodness–of-fit<br />
statistics for water level. NRMSE and NMAE values for the water levels<br />
range from 5-7%.<br />
<br />
[[File:Gironde_Water_Levels.png |thumb|right|400px|Figure 4. Comparison of measured and calculated water levels at five stations in the Gironde Estuary (stations shown in Figure 2).]]<br />
<br />
{| border="1"<br />
|+ Table 2. Water level goodness-of-fit statistics* for the Gironde Estuary test case.<br />
!Statistic !!Richard !!Lamena !!Pauillac !!Ile Verte !!La Reuille<br />
|-<br />
|NRMSE, % ||5.10 ||7.02 ||6.74 ||6.40 ||6.63<br />
|-<br />
|NMAE, % ||4.33 ||6.21 ||5.63 ||4.34 ||5.08<br />
|-<br />
|<math>R^2</math> ||0.982 ||0.956 ||0.951 ||0.962 ||0.972<br />
|-<br />
|Bias, m ||0.094 ||0.128 ||0.043 ||-0.060 ||-0.0252<br />
|}<br />
<br />
Figure 5 shows the comparison of the measured and simulated flow<br />
velocities at several stations (stations shown in Figure 2). The<br />
velocities were measured 1 m below the water surface and 1 m above the<br />
river bed, respectively. In this figure, positive current velocities<br />
correspond to flood tides and negative velocities to ebb tides. The<br />
current measurements at both elevations are relatively similar for all<br />
stations except Richard and Lamena. This might be due to baroclinic<br />
circulation produced by wind, fresh water intrusion, or other factors<br />
near these two stations.<br />
<br />
Some of the differences in water surface elevations and current<br />
velocities may be due to inaccuracies in the boundary conditions. The<br />
boundary conditions at the estuary entrance was obtained from a nearby<br />
station and therefore a slight phase lag of about 45 min was<br />
subtracted from calculated water surface elevations in order to match<br />
the measured time series. However, since the boundary condition used<br />
was not measured exactly at the location of the boundary, some error<br />
in phase lag may be expected from this approximation.<br />
<br />
Another probable source of error is the bottom roughness coefficient,<br />
which was assumed to be constant. Other field experiments show that<br />
the bottom roughness in an estuary can vary significantly due to<br />
changes in bed forms and grain sizes within the estuary. Although the<br />
CMS has the capability to use a spatially variable bottom roughness<br />
coefficient, there were no data available in this case. The agreement<br />
between measured and calculated current speeds is summarized in<br />
Table 3. NRMSE and NMAE in current speed range from 7-21%. Comparable<br />
results were obtained by Wu and Wang (2004) using a similar<br />
depth-averaged flow model.<br />
<br />
[[File:Gironde_Current_Speed.png |thumb|right|400px|Figure 5. Measured and calculated current speed in the Gironde Estuary (stations shown in Figure 2) ]]<br />
<br />
{| border="1"<br />
|+ Table 3. Current speed goodness of fit statistics for the Gironde Estuary test case.<br />
!Statistic !!Richard !!PK68 !!Lamena !!Pauillac-1 !!Pauillac-2 !!Blaye<br />
|NRMSE, % ||10.70 ||7.27 ||8.81 ||15.89 ||20.73 ||14.98<br />
|NMAE, % ||9.15 ||5.71 ||6.93 ||13.67 ||17.05 ||13.17<br />
|R2 ||0.911 ||0.957 ||0.968 ||0.856 ||0.680 ||0.804<br />
|Bias, m/s ||0.070 ||-0.057 ||0.062 ||0.022 ||-0.031 ||0.095<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
CMS calculations of tidal flow in a large estuary were compared to<br />
measured water level and current speed. Calculations agreed with<br />
measurements with errors ranging from 5-7% for water level and 7-21%<br />
for currents. The boundary condition used in the model was not<br />
measured exactly at the location of the boundary, and therefore the<br />
calculations incurred some error in phase lag of water surface<br />
elevation and in current velocities. This application demonstrates<br />
the accuracy of CMS within a macrotidal estuarine environment, for<br />
measurements distributed along the channel. It is recommended that the<br />
bottom roughness be estimated based on the bottom type (sandy, rocky<br />
outcrops, vegetation, etc.), and then adjusted (calibrated) based on<br />
field measurements of water levels and currents. When developing a new<br />
model setup and grid for engineering applications, it is useful to<br />
start simple as far as grid size and model forcing, and slow increase<br />
the model complexity, only as needed until satisfactory results are<br />
obtained for the purpose of the project. This iterative process has<br />
the added benefit of providing insights on the importance of physical<br />
processes and model sensitivity to setup parameters and grid geometry.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10608Li2014-04-22T19:16:09Z<p>U4hcsdaw: </p>
<hr />
<div><div><br />
<script> var a=1; </script><br />
<br />
</div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10607Li2014-04-22T19:15:09Z<p>U4hcsdaw: Replaced content with " <script> var a=1; </script>"</p>
<hr />
<div><br />
<br />
<br />
<br />
<script> var a=1; </script></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10606Li2014-04-22T18:17:25Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
|<br> <div style=" width:10ex; background-color:white; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Variable </div> <br> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NRMSE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NMAE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > <math>R^2</math> </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10605Li2014-04-22T18:16:38Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
|<br> <div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Variable </div> <br> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NRMSE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NMAE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > <math>R^2</math> </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10604Li2014-04-22T18:16:04Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
|<br> <br><div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Variable </div> <br> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NRMSE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NMAE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > <math>R^2</math> </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10603Li2014-04-22T18:15:32Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Variable </div> <br> <br> <br> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NRMSE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NMAE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > <math>R^2</math> </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10602Li2014-04-22T18:14:29Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Variable </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NRMSE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > NMAE,% </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > <math>R^2</math> </div> <br />
|<div style=" width:10ex; background-color:red; transform:rotate(-47deg); -ms-transform:rotate(-47deg); -webkit-transform:rotate(-47deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10601Li2014-04-22T18:12:20Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > b </div><br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > Variable </div> <br />
!!<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > NRMSE,% </div> <br />
!!<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > NMAE,% </div> <br />
!!<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > <math>R^2</math> </div> <br />
!!<div style=" width:10ex; background-color:red; transform:rotate(-7deg); -ms-transform:rotate(-7deg); -webkit-transform:rotate(-7deg);" > Bias </div> <br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10600Idealized jettied inlet2014-04-22T18:09:44Z<p>U4hcsdaw: /* Case 1 (H=1.65 m, T=11 s) */</p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png |thumb|right|600px|Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|600px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10599Li2014-04-22T18:06:26Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" width:10ex; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > b </div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10598Li2014-04-22T18:05:41Z<p>U4hcsdaw: </p>
<hr />
<div><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div><br />
<br />
<br />
<div style=" background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > b </div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10597Li2014-04-22T18:04:58Z<p>U4hcsdaw: </p>
<hr />
<div><style>div{<br />
width:200px;<br />
height:100px;<br />
background-color:red;<br />
/* Rotate div */<br />
transform:rotate(7deg);<br />
-ms-transform:rotate(7deg); /* IE 9 */<br />
-webkit-transform:rotate(7deg); /* Opera, Chrome, and Safari */<br />
}<br />
</style><br />
<br />
<br />
<br />
<div style="width:200px; height:100px; background-color:red; transform:rotate(7deg); -ms-transform:rotate(7deg); -webkit-transform:rotate(7deg);" > a </div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10596Li2014-04-22T18:04:07Z<p>U4hcsdaw: </p>
<hr />
<div><style>div{<br />
width:200px;<br />
height:100px;<br />
background-color:red;<br />
/* Rotate div */<br />
transform:rotate(7deg);<br />
-ms-transform:rotate(7deg); /* IE 9 */<br />
-webkit-transform:rotate(7deg); /* Opera, Chrome, and Safari */<br />
}<br />
</style><br />
<br />
a<br<br />
style="clear:both"<br />
/>b<br />
<br />
<div style="width:200px; height:100px; background-color:red; " > a </div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10595Li2014-04-22T18:03:33Z<p>U4hcsdaw: </p>
<hr />
<div><style>div{<br />
width:200px;<br />
height:100px;<br />
background-color:red;<br />
/* Rotate div */<br />
transform:rotate(7deg);<br />
-ms-transform:rotate(7deg); /* IE 9 */<br />
-webkit-transform:rotate(7deg); /* Opera, Chrome, and Safari */<br />
}<br />
</style><br />
<br />
a<br<br />
style="clear:both"<br />
/>b<br />
<br />
<div > a </div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10594Li2014-04-22T18:02:41Z<p>U4hcsdaw: </p>
<hr />
<div><style><br />
div<br />
{<br />
width:200px;<br />
height:100px;<br />
background-color:red;<br />
/* Rotate div */<br />
transform:rotate(7deg);<br />
-ms-transform:rotate(7deg); /* IE 9 */<br />
-webkit-transform:rotate(7deg); /* Opera, Chrome, and Safari */<br />
}<br />
</style><br />
<br />
a<br style="clear:both" />b</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10593Li2014-04-22T18:02:18Z<p>U4hcsdaw: </p>
<hr />
<div>a<br style="clear:both" />b</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Li&diff=10592Li2014-04-22T18:02:02Z<p>U4hcsdaw: Created page with "<br style="clear:both" />"</p>
<hr />
<div><br style="clear:both" /></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Test_Cases&diff=10591Test Cases2014-04-22T17:54:18Z<p>U4hcsdaw: /* Current-Wave Interaction */</p>
<hr />
<div><big><br />
__NOTOC__<br />
<font color=red>'''UNDER CONSTRUCTION'''</font><br />
== Hydrodynamics ==<br />
'''Analytical'''<br />
# [[Long wave propagation | Analytical Solution of long wave propagation in a Quarter Annulus (Lynch 1978)]]<br />
# [[Wind Setup | Analytical Solution for Wind Setup]]<br />
# [[Flow over a bump | Analytical Solution for Flow over a Bump]]<br />
# [[Long-wave Runup | Analytical Solution for Long-wave Runup over a Planar Slope (Carrier et al. 2003)]]<br />
# [[Circular Basin | Analytical Solution for Wind-driven Flow in a Circular Basin (Dupont 2001)]]<br />
# [[Standing wave in a rectangular basin | Analytical Solution for a Standing Wave in a Rectangular Basin (Lamb 1945)]]<br />
<br />
'''Laboratory'''<br />
# [[Spure Dike | Rectangular Flume with a Spure Dike (Rajaratnam and Nwachukwu 1983) ]]<br />
# [[Sudden Expansion | Rectangular Flume with Sudden Expansion (Xie 1996)]]<br />
# [[Nested Idealized Inlet]]<br />
# [[Planar Beach | Planar sloping beach with oblique incident regular wave]]<br />
# [[Idealized jettied inlet | Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves]]<br />
<br />
== Sediment Transport ==<br />
=== Channel Infilling ===<br />
# [[Channel infilling under steady currents | Channel infilling by currents (Galappatti and Vreugdenhil 1985)]]<br />
# [[Channel infilling under waves parallel to steady currents | Channel infilling by currents and waves parallel to flow (van Rijn 1986)]]<br />
# [[Channel infilling under waves perpendicular to steady currents | Channel infilling by currents and waves perpendicular to flow (van Rijn and Havinga 1993)]]<br />
<br />
=== Erosion Tests ===<br />
# [[Clear water jet | Clear water jet (Thuc 1991)]]<br />
<br />
=== Morphology Change ===<br />
# [[Morphology Change Validation of Shark River Inlet | Model Application to Shark River Inlet]]<br />
# [[Model Application to St. Augustine Inlet |Morphology Change Validation to St. Augustine Inlet]]<br />
<br />
=== Nonuniform Sediments ===<br />
# [[Deposition of Nonuniform Sediments | Downstream Fining of Nonuniform Sediments (Seal et al. 1995)]]<br />
<br />
== Salinity ==<br />
<br />
# [[Salinity | Salinity Transport Modeling at White Ditch Area, LA]]<br />
# [[Salinity Calculations in the Jupiter Inlet - Loxahatchee River System, FL]]<br />
<br />
== Structures==<br />
# [[Rubble Mound Tests | Rubble Mound Verification and Sensitivity]]<br />
# [[Weir Tests | Weir Application and Validation at Bonnet Carre Spillway, MS]]<br />
# [[Culvert Tests | Culvert Application and Validation at White Ditch, MS ]]<br />
# [[Structure | Evaluation of breakwaters and sedimentation at Dana Point Harbor, CA]]<br />
<br />
== Waves ==<br />
# [[Rosati, James | Mississippi Coastal Improvement Program (MsCIP) Validation to Wave Measurements ]]<br />
# [[Lab Wave Validation Case 1 | CMS-Wave 2008 - Lab Case 1 ]]<br />
# [[Lab Wave Validation Case 2 | CMS-Wave 2008 - Lab Case 2 ]]<br />
# [[Lab Wave Validation Case 3 | CMS-Wave 2008 - Lab Case 3 ]]<br />
# [[Field Experiment Wave Validation Case 1 | CMS-Wave 2008 - Field Case 1 ]]<br />
# [[Field Experiment Wave Validation Case 2 | CMS-Wave 2008 - Field Case 2 ]]<br />
# [[Field Experiment Wave Validation Case 3 | CMS-Wave 2008 - Field Case 3 ]]<br />
<br />
== Current-Wave Interaction ==<br />
# [[Visser | Regular Waves Breaking on a Planar Beach (Visser 1991)]]<br />
# [[LSTF | Random Waves Breaking on a Natural Beach (LSTF 2007)]]<br />
# [[Kuriyama_Ozaki | Random Waves Breaking on Barred Beach (Kuriyama and Ozaki 1993)]]<br />
# [[DELILAH | Random Waves Breaking on Barred Beach (Smith et al. 1993)]]<br />
# [[SEABERGH | Regular Waves on an Idealized Inlet (Seabergh et al. 2005)]]<br />
# [[Li | Gironde Estuary, France (Li et al. 1994).]]<br />
# [[Tri-Cusp Beach | Regular Waves Breaking on a Planar Beach with Three Cusps (Borthwick and Foote 2002)]]<br />
<br />
----<br />
<br />
[[CMS#Documentation_Portal | Documentation Portal]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10590Idealized jettied inlet2014-04-22T17:44:08Z<p>U4hcsdaw: /* Case 2 (H=2.0 m, T=11 s) */</p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png |thumb|right|600px|Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|600px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10589Idealized jettied inlet2014-04-22T17:43:28Z<p>U4hcsdaw: /* Case 3 (H=3.25 m, T=8 s) */</p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png |thumb|right|800px|Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|600px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10588Idealized jettied inlet2014-04-22T17:42:55Z<p>U4hcsdaw: /* Case 2 (H=2.0 m, T=11 s) */</p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png |thumb|right|800px|Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|400px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10587Idealized jettied inlet2014-04-21T22:56:32Z<p>U4hcsdaw: /* Case 2 (H=2.0 m, T=11 s) */</p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png |thumb|right|400px|Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|400px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Cross-Shore_Transects_Case3.png&diff=10586File:Cross-Shore Transects Case3.png2014-04-21T22:55:20Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=File:Cross-Shore_Currents_Case2.png&diff=10585File:Cross-Shore Currents Case2.png2014-04-21T22:54:01Z<p>U4hcsdaw: </p>
<hr />
<div></div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10584Idealized jettied inlet2014-04-21T22:53:11Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum equations.<br />
<br />
= Physical Experiment =<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
In 2005 the USACE conducted a physical model study to collect both current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 1 shows a map of the facility and basin area. A 1:50 undistorted Froude model scale was used to represent the dimensions of a medium-sized U.S. Atlantic coast inlet. The ocean side parallel contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is the still water depth, <math>x</math> is the cross-shore coordinate from the shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and previous modeling results with CMS the reader is referred to Seabergh et al. (2005) and Lin et al. (2008). Fully reflective and absorbing jetties were constructed for inlet geometries studied in the physical model. However, all of the tests shown here are for the absorbing jetties since they represent those typically found in coastal applications. The incident wave conditions for the test cases used here are shown in Table 1. The three cases were chosen to cover a wide range of wave heights.<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 1).<br />
**Clockwise from shore normal.<br />
<br />
<br style="clear:both" /><br />
<br />
= Model Setup =<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 2. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
The computational grid and bathymetry for both CMS-Flow and CMS-Wave is shown in Figure 2. The grid has 31,422 active cells and a constant resolution of 10 m (prototype scale). A list of the basic model setup parameters is given in Table 2. A constant zero water level boundary condition was assigned to the offshore boundary of CMS-Flow. A wall boundary condition was used at all boundaries inside the bay.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips (1977) and Svendson (2006). The formulation includes Stokes velocities in both the continuity and momentum equations and provides a better prediction of cross-shore currents.<br />
<br />
<br style="clear:both" /><br />
<br />
= Results and Discussion =<br />
The measured and calculated wave heights and wave-induced nearshore currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and cross-shore profiles are offset by a number indicated to left of each transect which are plotted using different colors. Demirbilek et al. (2009) reported similar results for the wave height using a previous version of CMS. The current velocities reported here are significantly improved with respect to Demirbilek et al. (2009) due to the implementation of the surface roller and Stokes velocities.<br />
<br />
<br style="clear:both" /><br />
== ''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s) ==<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 3. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
The calculated wave height magnitudes and directions agree well with the measurements with a NMAE of 10.62%(see Figures 3 and 4 and Table 3). The wave model tends to over predict wave refraction near the structure and shoreline. The breaker is located at approximately the third cross-shore measurement station from the shoreline and was well predicted by the model (Figure 3). Measured and computed current velocities for Case 1 are compared in Figures 5 and 6. The velocity field is characterized by a narrow longshore current approximately 75-m wide which is deflected seaward by the south jetty. The NRMSE and NMAE values for the longshore current are approximately 24 and 19%, respectively, while for the cross-shore current, they are significantly smaller at 14 and 10%, respectively (see Table 29). Most of the longshore current is located within the first 2 measurement stations from the shoreline. The calculated cross-shore currents agree well with the measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|left|400px|Figure 4. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
|}<br />
<br />
<br style="clear:both" /><br />
[[File:Cross-Shore_Transects_Measured.png |thumb|left|400px| Figure 5. Cross-shore transects of measured and calculated longshore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
[[File:Cross-Shore_Transects_Calculated.png |thumb|right|400px| Figure 6. Cross-shore transects of measured and calculated cross-shore currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br style="clear:both" /><br />
<br />
== Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s) ==<br />
The calculated wave height magnitudes and directions of Case 2 agree well with the measurements especially far away from the jetty (see<br />
Figures 7 and 8). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%, 8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty, the differences are larger possibly due to reflected wave energy from the jetty. Even though the jetties were made of small stones and absorbed most of the wave energy, a small portion of the wave energy was reflected. CMS-Wave has the capability to simulate reflecting waves. However, for this study it was assumed that the jetty reflectance was negligible. Additional tests will be conducted in the future to test this hypothesis. The breaker is located at approximately the fourth cross-shore measurement station from the shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 7. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 8. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along cross-sectional transects, shown in Figure 9, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone for Case 2 is wider than in Case 1, most of the long-shore current is still located within the first 3 measurement stations from the shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Case2.png ||leftthumb|400px| Figure 9. Cross-shore transects of measured and calculated long-shore currents for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br style="clear:both" /><br />
== Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s) ==<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 10. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 11. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
Figure 10 shows plan-view vector plots of the measured and computed wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are plotted in Figures 11 and 12. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well with the measurements with the exception of a few measurement stations where significant differences are observed in the incident wave angles. From the measurements it appears that the location of the breaker is outside of the measurement stations. The calculated longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively (Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be overestimated near the breaker.<br />
<br />
[[File:Cross-Shore_Transects_Case3.png |thumb|right|400px|Figure 12. Cross-shore transects of measured and calculated long-shore (left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.]]<br />
<br />
<br />
<br />
<br />
<br style="clear:both" /><br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br style="clear:both" /><br />
<br />
= Conclusions and Recommendations =<br />
Laboratory experiments were used to validate the CMS for cross-shore and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and wave-induced currents were compared with CMS simulations at the prototype scale. The CMS was run using mostly default settings, except for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held constant for all three cases. The value of the roller dissipation coefficient applied is the recommended value for regular waves. Model performance and behavior varied case by case but in general the calculated wave heights and wave-induced current velocities agreed reasonably well with measurements as indicated by the goodness-of-fit statistics. Calculated nearshore wave heights and currents upstream of a jetty were found to be within approximately 10-15% and 10-30%, respectively, of measurements. CMS-Wave was able to accurately predict the location of the wave breaker. However, tests were conducted in a physical model without tidal currents, winds, and with well known bathymetry and wave conditions which all represent additional potential sources of error in field applications. These results indicate that once the model is calibrated for a specific site, using mainly the bottom roughness, the model may be applied at the same site for different wave conditions without having to recalibrate the model. Using the wave- and depth-averaged hydrodynamic equations for depth-uniform currents as derived by Svendson (2006) significantly improved the nearshore currents most noticeably by producing an offshore directed flow or undertow. Including the surface roller improved the longshore currents by moving the peak longshore current closer to the shoreline.<br />
<br />
<br style="clear:both" /><br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10570Idealized jettied inlet2014-04-17T21:33:10Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for<br />
wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the<br />
inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum<br />
equations.<br />
<br />
= Physical Experiment =<br />
<br />
In 2005 the USACE conducted a physical model study to collect both<br />
current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was<br />
in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 24 shows a map of the facility and basin area. A 1:50<br />
undistorted Froude model scale was used to represent the dimensions of<br />
a medium-sized U.S. Atlantic coast inlet. The ocean side parallel<br />
contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is<br />
the still water depth, <math>x</math> is the cross-shore coordinate from the<br />
shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal<br />
to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and<br />
previous modeling results with CMS the reader is referred to Seabergh<br />
et al. (2005) and Lin et al. (2008). Fully reflective and absorbing<br />
jetties were constructed for inlet geometries studied in the physical<br />
model. However, all of the tests shown here are for the absorbing<br />
jetties since they represent those typically found in coastal<br />
applications. The incident wave conditions for the test cases used<br />
here are shown in Table 27. The three cases were chosen to cover a<br />
wide range of wave heights.<br />
<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|400px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 26).<br />
**Clockwise from shore normal.<br />
<br />
= Model Setup =<br />
<br />
The computational grid and bathymetry for both<br />
CMS-Flow and CMS-Wave is shown in Figure 26. The grid has 31,422<br />
active cells and a constant resolution of 10 m (prototype scale). A<br />
list of the basic model setup parameters is given in Table 28. A<br />
constant zero water level boundary condition was assigned to the<br />
offshore boundary of CMS-Flow. A wall boundary condition was used at<br />
all boundaries inside the bay.<br />
<br />
<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|400px|Figure 26. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s<br />
coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for<br />
this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the<br />
recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were<br />
held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the<br />
long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips<br />
(1977) and Svendson (2006). The formulation includes Stokes velocities<br />
in both the continuity and momentum equations and provides a better<br />
prediction of cross-shore currents.<br />
<br />
= Results and Discussion =<br />
<br />
The measured and calculated wave heights and wave-induced nearshore<br />
currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and<br />
cross-shore profiles are offset by a number indicated to left of each<br />
transect which are plotted using different colors. Demirbilek<br />
et al. (2009) reported similar results for the wave height using a<br />
previous version of CMS. The current velocities reported here are<br />
significantly improved with respect to Demirbilek et al. (2009) due to<br />
the implementation of the surface roller and Stokes velocities.<br />
<br />
''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and<br />
directions agree well with the measurements with a NMAE of 10.62%(see<br />
Figures 27 and 28 and Table 29). The wave model tends to over predict<br />
wave refraction near the structure and shoreline. The breaker is<br />
located at approximately the third cross-shore measurement station<br />
from the shoreline and was well predicted by the model<br />
(Figure 28). Measured and computed current velocities for Case 1 are<br />
compared in Figures 27 and 29. The velocity field is characterized by<br />
a narrow longshore current approximately 75-m wide which is deflected<br />
seaward by the south jetty. The NRMSE and NMAE values for the<br />
longshore current are approximately 24 and 19%, respectively, while<br />
for the cross-shore current, they are significantly smaller at 14 and<br />
10%, respectively (see Table 29). Most of the longshore current is<br />
located within the first 2 measurement stations from the<br />
shoreline. The calculated cross-shore currents agree well with the<br />
measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|400px|Figure 2. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|right|400px|Figure 3. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
<br />
[[File:Cross-Shore_Transects_Measured.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Transects_Calculated.png ||rightthumb|400px|alt=framework]]<br />
Figure 4. Cross-shore transects of measured and calculated longshore (left) and cross-shore (right) currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics* for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
*defined in Appendix A<br />
|}<br />
<br />
<br />
Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and directions of Case 2 agree<br />
well with the measurements especially far away from the jetty (see<br />
Figures 30 and 31). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%,<br />
8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty,<br />
the differences are larger possibly due to reflected wave energy from<br />
the jetty. Even though the jetties were made of small stones and<br />
absorbed most of the wave energy, a small portion of the wave energy<br />
was reflected. CMS-Wave has the capability to simulate reflecting<br />
waves. However, for this study it was assumed that the jetty<br />
reflectance was negligible. Additional tests will be conducted in the<br />
future to test this hypothesis. The breaker is located at<br />
approximately the fourth cross-shore measurement station from the<br />
shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|400px|Figure 5. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|400px|Figure 6. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along<br />
cross-sectional transects, shown in Figure 32, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone<br />
for Case 2 is wider than in Case 1, most of the long-shore current is<br />
still located within the first 3 measurement stations from the<br />
shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside<br />
of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case2.png |thumb|left|400px|]]<br />
[[File:Cross-Shore_Currents_Calculated_Case2.png |thumb|right|400px|]]<br />
Figure 7. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 2<br />
(<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes,<br />
current velocities are shifted by the number indicated on the left<br />
hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br />
Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
<br />
Figure 33 shows plan-view vector plots of the measured and computed<br />
wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are<br />
plotted in Figures 34 and 35. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement<br />
locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave<br />
breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well<br />
with the measurements with the exception of a few measurement stations<br />
where significant differences are observed in the incident wave<br />
angles. From the measurements it appears that the location of the<br />
breaker is outside of the measurement stations. The calculated<br />
longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore<br />
velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively<br />
(Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be<br />
overestimated near the breaker.<br />
<br />
<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 8. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 9. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case3.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Currents_Calculated_Case3.png ||rightthumb|400px|alt=framework]]<br />
Figure 10. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the<br />
number indicated on the left hand side of each transect.<br />
<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Laboratory experiments were used to validate the CMS for cross-shore<br />
and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and<br />
wave-induced currents were compared with CMS simulations at the<br />
prototype scale. The CMS was run using mostly default settings, except<br />
for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held<br />
constant for all three cases. The value of the roller dissipation<br />
coefficient applied is the recommended value for regular waves. Model<br />
performance and behavior varied case by case but in general the<br />
calculated wave heights and wave-induced current velocities agreed<br />
reasonably well with measurements as indicated by the goodness-of-fit<br />
statistics. Calculated nearshore wave heights and currents upstream of<br />
a jetty were found to be within approximately 10-15% and 10-30%,<br />
respectively, of measurements. CMS-Wave was able to accurately predict<br />
the location of the wave breaker. However, tests were conducted in a<br />
physical model without tidal currents, winds, and with well known<br />
bathymetry and wave conditions which all represent additional<br />
potential sources of error in field applications. These results<br />
indicate that once the model is calibrated for a specific site, using<br />
mainly the bottom roughness, the model may be applied at the same site<br />
for different wave conditions without having to recalibrate the<br />
model. Using the wave- and depth-averaged hydrodynamic equations for<br />
depth-uniform currents as derived by Svendson (2006) significantly<br />
improved the nearshore currents most noticeably by producing an<br />
offshore directed flow or undertow. Including the surface roller<br />
improved the longshore currents by moving the peak longshore current<br />
closer to the shoreline.<br />
<br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10569Idealized jettied inlet2014-04-17T21:28:12Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for<br />
wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the<br />
inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum<br />
equations.<br />
<br />
= Physical Experiment =<br />
<br />
In 2005 the USACE conducted a physical model study to collect both<br />
current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was<br />
in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 24 shows a map of the facility and basin area. A 1:50<br />
undistorted Froude model scale was used to represent the dimensions of<br />
a medium-sized U.S. Atlantic coast inlet. The ocean side parallel<br />
contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is<br />
the still water depth, <math>x</math> is the cross-shore coordinate from the<br />
shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal<br />
to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and<br />
previous modeling results with CMS the reader is referred to Seabergh<br />
et al. (2005) and Lin et al. (2008). Fully reflective and absorbing<br />
jetties were constructed for inlet geometries studied in the physical<br />
model. However, all of the tests shown here are for the absorbing<br />
jetties since they represent those typically found in coastal<br />
applications. The incident wave conditions for the test cases used<br />
here are shown in Table 27. The three cases were chosen to cover a<br />
wide range of wave heights.<br />
<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|600px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 26).<br />
**Clockwise from shore normal.<br />
<br />
= Model Setup =<br />
<br />
The computational grid and bathymetry for both<br />
CMS-Flow and CMS-Wave is shown in Figure 26. The grid has 31,422<br />
active cells and a constant resolution of 10 m (prototype scale). A<br />
list of the basic model setup parameters is given in Table 28. A<br />
constant zero water level boundary condition was assigned to the<br />
offshore boundary of CMS-Flow. A wall boundary condition was used at<br />
all boundaries inside the bay.<br />
<br />
<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|600px|Figure 26. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s<br />
coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for<br />
this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the<br />
recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were<br />
held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the<br />
long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips<br />
(1977) and Svendson (2006). The formulation includes Stokes velocities<br />
in both the continuity and momentum equations and provides a better<br />
prediction of cross-shore currents.<br />
<br />
= Results and Discussion =<br />
<br />
The measured and calculated wave heights and wave-induced nearshore<br />
currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and<br />
cross-shore profiles are offset by a number indicated to left of each<br />
transect which are plotted using different colors. Demirbilek<br />
et al. (2009) reported similar results for the wave height using a<br />
previous version of CMS. The current velocities reported here are<br />
significantly improved with respect to Demirbilek et al. (2009) due to<br />
the implementation of the surface roller and Stokes velocities.<br />
<br />
''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and<br />
directions agree well with the measurements with a NMAE of 10.62%(see<br />
Figures 27 and 28 and Table 29). The wave model tends to over predict<br />
wave refraction near the structure and shoreline. The breaker is<br />
located at approximately the third cross-shore measurement station<br />
from the shoreline and was well predicted by the model<br />
(Figure 28). Measured and computed current velocities for Case 1 are<br />
compared in Figures 27 and 29. The velocity field is characterized by<br />
a narrow longshore current approximately 75-m wide which is deflected<br />
seaward by the south jetty. The NRMSE and NMAE values for the<br />
longshore current are approximately 24 and 19%, respectively, while<br />
for the cross-shore current, they are significantly smaller at 14 and<br />
10%, respectively (see Table 29). Most of the longshore current is<br />
located within the first 2 measurement stations from the<br />
shoreline. The calculated cross-shore currents agree well with the<br />
measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 2. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|right|600px|Figure 3. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
<br />
[[File:Cross-Shore_Transects_Measured.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Transects_Calculated.png ||rightthumb|400px|alt=framework]]<br />
Figure 4. Cross-shore transects of measured and calculated longshore (left) and cross-shore (right) currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics* for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
*defined in Appendix A<br />
|}<br />
<br />
<br />
Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and directions of Case 2 agree<br />
well with the measurements especially far away from the jetty (see<br />
Figures 30 and 31). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%,<br />
8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty,<br />
the differences are larger possibly due to reflected wave energy from<br />
the jetty. Even though the jetties were made of small stones and<br />
absorbed most of the wave energy, a small portion of the wave energy<br />
was reflected. CMS-Wave has the capability to simulate reflecting<br />
waves. However, for this study it was assumed that the jetty<br />
reflectance was negligible. Additional tests will be conducted in the<br />
future to test this hypothesis. The breaker is located at<br />
approximately the fourth cross-shore measurement station from the<br />
shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|600px|Figure 5. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|600px|Figure 6. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along<br />
cross-sectional transects, shown in Figure 32, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone<br />
for Case 2 is wider than in Case 1, most of the long-shore current is<br />
still located within the first 3 measurement stations from the<br />
shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside<br />
of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case2.png |thumb|left|600px|]]<br />
[[File:Cross-Shore_Currents_Calculated_Case2.png |thumb|right|600px|]]<br />
Figure 7. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 2<br />
(<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes,<br />
current velocities are shifted by the number indicated on the left<br />
hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br />
Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
<br />
Figure 33 shows plan-view vector plots of the measured and computed<br />
wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are<br />
plotted in Figures 34 and 35. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement<br />
locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave<br />
breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well<br />
with the measurements with the exception of a few measurement stations<br />
where significant differences are observed in the incident wave<br />
angles. From the measurements it appears that the location of the<br />
breaker is outside of the measurement stations. The calculated<br />
longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore<br />
velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively<br />
(Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be<br />
overestimated near the breaker.<br />
<br />
<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 8. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 9. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case3.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Currents_Calculated_Case3.png ||rightthumb|400px|alt=framework]]<br />
Figure 10. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the<br />
number indicated on the left hand side of each transect.<br />
<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Laboratory experiments were used to validate the CMS for cross-shore<br />
and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and<br />
wave-induced currents were compared with CMS simulations at the<br />
prototype scale. The CMS was run using mostly default settings, except<br />
for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held<br />
constant for all three cases. The value of the roller dissipation<br />
coefficient applied is the recommended value for regular waves. Model<br />
performance and behavior varied case by case but in general the<br />
calculated wave heights and wave-induced current velocities agreed<br />
reasonably well with measurements as indicated by the goodness-of-fit<br />
statistics. Calculated nearshore wave heights and currents upstream of<br />
a jetty were found to be within approximately 10-15% and 10-30%,<br />
respectively, of measurements. CMS-Wave was able to accurately predict<br />
the location of the wave breaker. However, tests were conducted in a<br />
physical model without tidal currents, winds, and with well known<br />
bathymetry and wave conditions which all represent additional<br />
potential sources of error in field applications. These results<br />
indicate that once the model is calibrated for a specific site, using<br />
mainly the bottom roughness, the model may be applied at the same site<br />
for different wave conditions without having to recalibrate the<br />
model. Using the wave- and depth-averaged hydrodynamic equations for<br />
depth-uniform currents as derived by Svendson (2006) significantly<br />
improved the nearshore currents most noticeably by producing an<br />
offshore directed flow or undertow. Including the surface roller<br />
improved the longshore currents by moving the peak longshore current<br />
closer to the shoreline.<br />
<br />
= References =<br />
* Demirbilek, Z., Lin, L., Seabergh, W.C. (2009). “Laboratory and numerical modeling studies of hydrodynamics near jetties,” Coastal Engineering Journal, 51(2), 143-175.<br />
* Lin, L., Z. Demirbilek, H. Mase, and J. Zheng. (2008). “CMS-Wave: A nearshore spectral wave processes model for coastal inlets and navigation projects,” Technical Report ERDC/CHL TR-08-13, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS.<br />
* Phillips, O.M. (1977) "Dynamics of the upper ocean," Cambridge University Press. 261 p,<br />
* Seabergh, W. C., Lin, L., Demirbilek, Z. (2005). “Laboratory study of hydrodynamics near absorbing and fully reflecting jetties,” Technical Report ERDC/CHL (in press), Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.<br />
* Svendsen, I.A. (2006). "Introduction to nearshore hydrodynamics," Advanced Series on Ocean Engineering, 124, World Scientific Publishing, 722 p.<br />
<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10568Idealized jettied inlet2014-04-17T21:21:14Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for<br />
wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the<br />
inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum<br />
equations.<br />
<br />
= Physical Experiment =<br />
<br />
In 2005 the USACE conducted a physical model study to collect both<br />
current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was<br />
in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 24 shows a map of the facility and basin area. A 1:50<br />
undistorted Froude model scale was used to represent the dimensions of<br />
a medium-sized U.S. Atlantic coast inlet. The ocean side parallel<br />
contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is<br />
the still water depth, <math>x</math> is the cross-shore coordinate from the<br />
shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal<br />
to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and<br />
previous modeling results with CMS the reader is referred to Seabergh<br />
et al. (2005) and Lin et al. (2006). Fully reflective and absorbing<br />
jetties were constructed for inlet geometries studied in the physical<br />
model. However, all of the tests shown here are for the absorbing<br />
jetties since they represent those typically found in coastal<br />
applications. The incident wave conditions for the test cases used<br />
here are shown in Table 27. The three cases were chosen to cover a<br />
wide range of wave heights.<br />
<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|600px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
<br />
<br />
{| border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 26).<br />
**Clockwise from shore normal.<br />
<br />
= Model Setup =<br />
<br />
The computational grid and bathymetry for both<br />
CMS-Flow and CMS-Wave is shown in Figure 26. The grid has 31,422<br />
active cells and a constant resolution of 10 m (prototype scale). A<br />
list of the basic model setup parameters is given in Table 28. A<br />
constant zero water level boundary condition was assigned to the<br />
offshore boundary of CMS-Flow. A wall boundary condition was used at<br />
all boundaries inside the bay.<br />
<br />
<br />
[[File:Idealized_Inlet_Computational_Grid.png |thumb|right|600px|Figure 26. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.]]<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s<br />
coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for<br />
this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the<br />
recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were<br />
held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the<br />
long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips<br />
(1977) and Svendson (2006). The formulation includes Stokes velocities<br />
in both the continuity and momentum equations and provides a better<br />
prediction of cross-shore currents.<br />
<br />
= Results and Discussion =<br />
<br />
The measured and calculated wave heights and wave-induced nearshore<br />
currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and<br />
cross-shore profiles are offset by a number indicated to left of each<br />
transect which are plotted using different colors. Demirbilek<br />
et al. (2009) reported similar results for the wave height using a<br />
previous version of CMS. The current velocities reported here are<br />
significantly improved with respect to Demirbilek et al. (2009) due to<br />
the implementation of the surface roller and Stokes velocities.<br />
<br />
''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and<br />
directions agree well with the measurements with a NMAE of 10.62%(see<br />
Figures 27 and 28 and Table 29). The wave model tends to over predict<br />
wave refraction near the structure and shoreline. The breaker is<br />
located at approximately the third cross-shore measurement station<br />
from the shoreline and was well predicted by the model<br />
(Figure 28). Measured and computed current velocities for Case 1 are<br />
compared in Figures 27 and 29. The velocity field is characterized by<br />
a narrow longshore current approximately 75-m wide which is deflected<br />
seaward by the south jetty. The NRMSE and NMAE values for the<br />
longshore current are approximately 24 and 19%, respectively, while<br />
for the cross-shore current, they are significantly smaller at 14 and<br />
10%, respectively (see Table 29). Most of the longshore current is<br />
located within the first 2 measurement stations from the<br />
shoreline. The calculated cross-shore currents agree well with the<br />
measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights.png |thumb|right|600px|Figure 2. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.]]<br />
<br />
<br />
[[File:Cross-Shore_Transects.png |thumb|right|600px|Figure 3. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
<br />
[[File:Cross-Shore_Transects_Measured.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Transects_Calculated.png ||rightthumb|400px|alt=framework]]<br />
Figure 4. Cross-shore transects of measured and calculated longshore (left) and cross-shore (right) currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics* for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
*defined in Appendix A<br />
|}<br />
<br />
<br />
Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and directions of Case 2 agree<br />
well with the measurements especially far away from the jetty (see<br />
Figures 30 and 31). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%,<br />
8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty,<br />
the differences are larger possibly due to reflected wave energy from<br />
the jetty. Even though the jetties were made of small stones and<br />
absorbed most of the wave energy, a small portion of the wave energy<br />
was reflected. CMS-Wave has the capability to simulate reflecting<br />
waves. However, for this study it was assumed that the jetty<br />
reflectance was negligible. Additional tests will be conducted in the<br />
future to test this hypothesis. The breaker is located at<br />
approximately the fourth cross-shore measurement station from the<br />
shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png |thumb|right|600px|Figure 5. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
]]<br />
<br />
[[File:Cross-Shore_Transects_Case2.png |thumb|right|600px|Figure 6. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.]]<br />
<br />
<br />
Measured and calculated current velocities for Case 2 along<br />
cross-sectional transects, shown in Figure 32, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone<br />
for Case 2 is wider than in Case 1, most of the long-shore current is<br />
still located within the first 3 measurement stations from the<br />
shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside<br />
of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case2.png |thumb|left|600px|]]<br />
[[File:Cross-Shore_Currents_Calculated_Case2.png |thumb|right|600px|]]<br />
Figure 7. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 2<br />
(<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes,<br />
current velocities are shifted by the number indicated on the left<br />
hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br />
Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
<br />
Figure 33 shows plan-view vector plots of the measured and computed<br />
wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are<br />
plotted in Figures 34 and 35. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement<br />
locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave<br />
breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well<br />
with the measurements with the exception of a few measurement stations<br />
where significant differences are observed in the incident wave<br />
angles. From the measurements it appears that the location of the<br />
breaker is outside of the measurement stations. The calculated<br />
longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore<br />
velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively<br />
(Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be<br />
overestimated near the breaker.<br />
<br />
<br />
[[File:Measured_Calculated_Wave_Height_Case3.png |thumb|right|600px|Figure 8. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.]]<br />
<br />
<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png |thumb|right|600px|Figure 9. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.]]<br />
<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case3.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Currents_Calculated_Case3.png ||rightthumb|400px|alt=framework]]<br />
Figure 10. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the<br />
number indicated on the left hand side of each transect.<br />
<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Laboratory experiments were used to validate the CMS for cross-shore<br />
and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and<br />
wave-induced currents were compared with CMS simulations at the<br />
prototype scale. The CMS was run using mostly default settings, except<br />
for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held<br />
constant for all three cases. The value of the roller dissipation<br />
coefficient applied is the recommended value for regular waves. Model<br />
performance and behavior varied case by case but in general the<br />
calculated wave heights and wave-induced current velocities agreed<br />
reasonably well with measurements as indicated by the goodness-of-fit<br />
statistics. Calculated nearshore wave heights and currents upstream of<br />
a jetty were found to be within approximately 10-15% and 10-30%,<br />
respectively, of measurements. CMS-Wave was able to accurately predict<br />
the location of the wave breaker. However, tests were conducted in a<br />
physical model without tidal currents, winds, and with well known<br />
bathymetry and wave conditions which all represent additional<br />
potential sources of error in field applications. These results<br />
indicate that once the model is calibrated for a specific site, using<br />
mainly the bottom roughness, the model may be applied at the same site<br />
for different wave conditions without having to recalibrate the<br />
model. Using the wave- and depth-averaged hydrodynamic equations for<br />
depth-uniform currents as derived by Svendson (2006) significantly<br />
improved the nearshore currents most noticeably by producing an<br />
offshore directed flow or undertow. Including the surface roller<br />
improved the longshore currents by moving the peak longshore current<br />
closer to the shoreline.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Idealized_jettied_inlet&diff=10567Idealized jettied inlet2014-04-17T21:16:51Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex4: Idealized jettied inlet with equilibrium beach profile and oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The purpose of this validation case was to evaluate the CMS for<br />
wave-induced hydrodynamics in the vicinity of an inlet with two<br />
absorbing jetties. The specific model features to be tested are the<br />
inline flow and wave coupling, wave-adjusted lateral boundary<br />
conditions, and Stokes velocities in the continuity and momentum<br />
equations.<br />
<br />
= Physical Experiment =<br />
<br />
In 2005 the USACE conducted a physical model study to collect both<br />
current and wave measurements in the vicinity of an idealized dual<br />
jetty inlet (Seabergh et al. 2005). The idealized inlet experiment was<br />
in a 46-m wide by 99-m long concrete basin with 0.6-m high<br />
walls. Figure 24 shows a map of the facility and basin area. A 1:50<br />
undistorted Froude model scale was used to represent the dimensions of<br />
a medium-sized U.S. Atlantic coast inlet. The ocean side parallel<br />
contours correspond to an equilibrium profile <math>h=Ax^{2/3}</math>, where h is<br />
the still water depth, <math>x</math> is the cross-shore coordinate from the<br />
shoreline and <math>A</math> is a grain size dependant empirical coefficient (equal<br />
to 0.1615 m<math>^{1/3}</math> here). For further details on the physical model and<br />
previous modeling results with CMS the reader is referred to Seabergh<br />
et al. (2005) and Lin et al. (2006). Fully reflective and absorbing<br />
jetties were constructed for inlet geometries studied in the physical<br />
model. However, all of the tests shown here are for the absorbing<br />
jetties since they represent those typically found in coastal<br />
applications. The incident wave conditions for the test cases used<br />
here are shown in Table 27. The three cases were chosen to cover a<br />
wide range of wave heights.<br />
<br />
[[File:Idealized_Inlet_Model_Setup.png |thumb|right|600px|Figure 1. Physical model setup for the idealized inlet case (from Seabergh et al. (2005).]]<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 1. Wave conditions (prototype scale) of three test cases from Seabergh et al. (2005).<br />
!Case !!Wave height*, m !!Wave period, s !!Wave Direction**<br />
|-<br />
|1|| 1.65 || 11.0|| -20º<br />
|-<br />
|2|| 2.0 || 11.0|| -20º<br />
|-<br />
|3|| 3.25 || 8.0 || -20º<br />
|}<br />
*Measured at the first offshore station approximately 50 m (prototype) from the jetty tips (see Figure 26).<br />
**Clockwise from shore normal.<br />
<br />
= Model Setup =<br />
<br />
The computational grid and bathymetry for both<br />
CMS-Flow and CMS-Wave is shown in Figure 26. The grid has 31,422<br />
active cells and a constant resolution of 10 m (prototype scale). A<br />
list of the basic model setup parameters is given in Table 28. A<br />
constant zero water level boundary condition was assigned to the<br />
offshore boundary of CMS-Flow. A wall boundary condition was used at<br />
all boundaries inside the bay.<br />
<br />
<br />
[[File:Idealized_Inlet_Computational_Grid.png ||leftthumb|400px|alt=framework]]<br />
Figure 26. CMS computational grid showing the model bathymetry. Black<br />
circles indicate current velocity and wave height measurement stations<br />
used in this study.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 2. CMS settings for the Seabergh et al. (2005) experiment.<br />
!Parameter !!Value<br />
|-<br />
|Flow time step || 6 min<br />
|-<br />
|Simulation duration || 4 hr<br />
|-<br />
|Ramp period duration || 3 hr<br />
|-<br />
|Manning’s n (both flow and wave grids) ||0.025 s/m1/3<br />
|-<br />
|Steering interval || 1 hr<br />
|-<br />
|Roller || On<br />
|-<br />
|Roller dissipation coefficient || 0.05 (default for regular waves)<br />
|-<br />
|Stokes velocities ||On<br />
|-<br />
|Wave reflection coefficient ||0.0<br />
|}<br />
<br />
<br />
Default CMS settings were used where possible with the Manning’s<br />
coefficient being the only calibrated parameter (<math>n</math> = 0.025 s/m<math>^{1/3}</math>) for<br />
this case study. The roller dissipation coefficient <math>\beta_D</math> was set to the<br />
recommended value for regular waves (<math>\beta_D</math>= 0.05). Both parameters were<br />
held constant for all test cases. Including the roller is very<br />
important for regular waves because it improves the prediction of the<br />
long-shore current. The wave- and depth-averaged hydrodynamics<br />
equations are solved for depth-uniform currents according to Phillips<br />
(1977) and Svendson (2006). The formulation includes Stokes velocities<br />
in both the continuity and momentum equations and provides a better<br />
prediction of cross-shore currents.<br />
<br />
= Results and Discussion =<br />
<br />
The measured and calculated wave heights and wave-induced nearshore<br />
currents are presented in plan view vector plots and also cross-shore<br />
transects as discussed below. Note that the wave height and<br />
cross-shore profiles are offset by a number indicated to left of each<br />
transect which are plotted using different colors. Demirbilek<br />
et al. (2009) reported similar results for the wave height using a<br />
previous version of CMS. The current velocities reported here are<br />
significantly improved with respect to Demirbilek et al. (2009) due to<br />
the implementation of the surface roller and Stokes velocities.<br />
<br />
''Case 1'' (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and<br />
directions agree well with the measurements with a NMAE of 10.62%(see<br />
Figures 27 and 28 and Table 29). The wave model tends to over predict<br />
wave refraction near the structure and shoreline. The breaker is<br />
located at approximately the third cross-shore measurement station<br />
from the shoreline and was well predicted by the model<br />
(Figure 28). Measured and computed current velocities for Case 1 are<br />
compared in Figures 27 and 29. The velocity field is characterized by<br />
a narrow longshore current approximately 75-m wide which is deflected<br />
seaward by the south jetty. The NRMSE and NMAE values for the<br />
longshore current are approximately 24 and 19%, respectively, while<br />
for the cross-shore current, they are significantly smaller at 14 and<br />
10%, respectively (see Table 29). Most of the longshore current is<br />
located within the first 2 measurement stations from the<br />
shoreline. The calculated cross-shore currents agree well with the<br />
measurements except near the jetty where it was overestimated.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights.png ||leftthumb|400px|alt=framework]]<br />
Figure 2. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 1. Background colors indicate the local water<br />
depth corresponding to the right color bar.<br />
<br />
[[File:Cross-Shore_Transects.png ||leftthumb|400px|alt=framework]]<br />
Figure 3. Cross-shore transects of measured and calculated wave<br />
heights for Case 1 (<math>H</math> = 1.65 m, <math>T</math>= 11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.<br />
<br />
<br />
[[File:Cross-Shore_Transects_Measured.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Transects_Calculated.png ||rightthumb|400px|alt=framework]]<br />
Figure 4. Cross-shore transects of measured and calculated longshore (left) and cross-shore (right) currents for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s). For display purposes, current velocities are shifted by the number indicated on the left hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 3. Goodness-of-fit statistics* for Case 1 (<math>H</math>=1.65 m, <math>T</math>=11 s)<br />
!Variable !!NRMSE,% !!NMAE,% !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||24.11 ||18.74 ||0.836 ||-0.141 m/s<br />
|- <br />
|Cross-shore current ||14.27 ||10.30 ||0.907 ||0.017 m/s<br />
|- <br />
|Wave Height ||13.96 ||10.62 ||0.826 ||0.051 m<br />
|- <br />
*defined in Appendix A<br />
|}<br />
<br />
<br />
Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s)<br />
<br />
The calculated wave height magnitudes and directions of Case 2 agree<br />
well with the measurements especially far away from the jetty (see<br />
Figures 30 and 31). The wave height NRMSE, NMAE, and <math>R^2</math> are 12.33%,<br />
8.05 %, and 0.889, respectively (see Table 30). Closer to the jetty,<br />
the differences are larger possibly due to reflected wave energy from<br />
the jetty. Even though the jetties were made of small stones and<br />
absorbed most of the wave energy, a small portion of the wave energy<br />
was reflected. CMS-Wave has the capability to simulate reflecting<br />
waves. However, for this study it was assumed that the jetty<br />
reflectance was negligible. Additional tests will be conducted in the<br />
future to test this hypothesis. The breaker is located at<br />
approximately the fourth cross-shore measurement station from the<br />
shoreline and was well predicted by the model.<br />
<br />
[[File:Idealized_Inlet_Wave_Heights_Case2.png ||leftthumb|400px|alt=framework]]<br />
Figure 5. Measured and calculate wave height (left) and mean current<br />
(right) vectors for Case 2. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
<br />
<br />
[[File:Cross-Shore_Transects_Case2.png ||leftthumb|400px|alt=framework]]<br />
Figure 6. Cross-shore transects of measured and calculated wave<br />
heights for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes, wave<br />
heights are shifted by the number indicated on the left hand side of<br />
each transect.<br />
<br />
Measured and calculated current velocities for Case 2 along<br />
cross-sectional transects, shown in Figure 32, have NRMSE and NMAE<br />
values less than 15 and 13%, respectively. Although the breaker zone<br />
for Case 2 is wider than in Case 1, most of the long-shore current is<br />
still located within the first 3 measurement stations from the<br />
shoreline. The calculated cross-shore currents tend to be<br />
underestimated near the shoreline and slightly overestimated outside<br />
of the breaker for all cross-shore transects except the one adjacent<br />
to the jetty.<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case2.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Currents_Calculated_Case2.png ||rightthumb|400px|alt=framework]]<br />
Figure 7. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 2<br />
(<math>H</math>=2.0 m, <math>T</math>=11 s). For display purposes,<br />
current velocities are shifted by the number indicated on the left<br />
hand side of each transect.<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 4. Goodness-of-fit statistics* for Case 2 (<math>H</math>=2.0 m, <math>T</math>=11s)<br />
!Variable !!NRMSE,% !!NMAE,% !!R2 !!Bias<br />
|- <br />
|Longshore current ||14.43 ||12.24 ||0.797 ||-0.007 m/s<br />
|- <br />
|Cross-shore current ||14.69 ||11.49 ||0.930 ||-0.065 m/s<br />
|- <br />
|Wave Height ||12.33 ||8.05 ||0.889 ||-0.040 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
<br />
<br />
Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
<br />
Figure 33 shows plan-view vector plots of the measured and computed<br />
wave heights and current velocities for Case 3. Cross-shore profiles<br />
of measured and computed wave heights and current velocities are<br />
plotted in Figures 34 and 35. For this case, the calculated wave<br />
heights are slightly overestimated for most of the measurement<br />
locations indicating the wave breaker coefficient was slightly<br />
overestimated for this steep wave condition. It is noted that wave<br />
breaker coefficient calculation is intended for irregular waves and<br />
has not been calibrated for regular waves. Wave directions agree well<br />
with the measurements with the exception of a few measurement stations<br />
where significant differences are observed in the incident wave<br />
angles. From the measurements it appears that the location of the<br />
breaker is outside of the measurement stations. The calculated<br />
longshore current velocities show the smallest NRMSE and NMAE of all<br />
three cases with values of 14 and 11%, respectively. The cross-shore<br />
velocities conversely, show the largest NRMSE and NMAE values of all<br />
three cases with values of 28 and 20%, respectively<br />
(Table 31). Measured and computed current velocities for Case 3 agree<br />
reasonably well. However, the long-shore current speed tends to be<br />
overestimated near the breaker.<br />
<br />
<br />
[[File:Measured_Calculated_Wave_Height_Case3.png ||leftthumb|400px|alt=framework]]<br />
Figure 8. Measured and calculated wave height (left) and mean current<br />
(right) vectors for Case 3. Background colors indicate the local water<br />
depth corresponding the right color bar.<br />
<br />
<br />
[[File:Measured_Calculated_Transects_Case3.png ||leftthumb|400px|alt=framework]]<br />
Figure 9. Cross-shore transects of measured and calculated wave<br />
heights for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For<br />
display purposes, wave heights are shifted by the number indicated on<br />
the left hand side of each transect.<br />
<br />
[[File:Cross-Shore_Currents_Measured_Case3.png ||leftthumb|400px|alt=framework]]<br />
[[File:Cross-Shore_Currents_Calculated_Case3.png ||rightthumb|400px|alt=framework]]<br />
Figure 10. Cross-shore transects of measured and calculated long-shore<br />
(left) and cross-shore (right) currents for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s). For display purposes, current velocities are shifted by the<br />
number indicated on the left hand side of each transect.<br />
<br />
<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|+ Table 5. Goodness-of-fit statistics* for Case 3 (<math>H</math>=3.25 m, <math>T</math>=8 s)<br />
!Variable !!NRMSE, % !!RMAE, % !!<math>R^2</math> !!Bias<br />
|- <br />
|Longshore current ||13.86 ||10.61 ||0.886 ||-0.189 m/s<br />
|- <br />
|Cross-shore current ||27.75 ||20.48 ||0.676 ||0.158 m/s<br />
|- <br />
|Wave Height ||9.98 ||8.68 ||0.978 ||0.223 m<br />
|- <br />
|*defined in Appendix A<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Laboratory experiments were used to validate the CMS for cross-shore<br />
and longshore currents and waves near an idealized inlet with two<br />
fully-absorbing jetties. Measurements of regular waves and<br />
wave-induced currents were compared with CMS simulations at the<br />
prototype scale. The CMS was run using mostly default settings, except<br />
for the Manning’s coefficient ((<math>n</math> = 0.025 s/m1/3) and roller<br />
dissipation coefficient (<math>\Beta_D</math> = 0.05). Both parameters were held<br />
constant for all three cases. The value of the roller dissipation<br />
coefficient applied is the recommended value for regular waves. Model<br />
performance and behavior varied case by case but in general the<br />
calculated wave heights and wave-induced current velocities agreed<br />
reasonably well with measurements as indicated by the goodness-of-fit<br />
statistics. Calculated nearshore wave heights and currents upstream of<br />
a jetty were found to be within approximately 10-15% and 10-30%,<br />
respectively, of measurements. CMS-Wave was able to accurately predict<br />
the location of the wave breaker. However, tests were conducted in a<br />
physical model without tidal currents, winds, and with well known<br />
bathymetry and wave conditions which all represent additional<br />
potential sources of error in field applications. These results<br />
indicate that once the model is calibrated for a specific site, using<br />
mainly the bottom roughness, the model may be applied at the same site<br />
for different wave conditions without having to recalibrate the<br />
model. Using the wave- and depth-averaged hydrodynamic equations for<br />
depth-uniform currents as derived by Svendson (2006) significantly<br />
improved the nearshore currents most noticeably by producing an<br />
offshore directed flow or undertow. Including the surface roller<br />
improved the longshore currents by moving the peak longshore current<br />
closer to the shoreline.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10566Planar Beach2014-04-17T21:13:31Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 1.<br />
<br />
{|border="1"<br />
|+ Table 1. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 1) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 2<br />
and 3 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png |thumb|right|400px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 2. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 3. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 4. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 2. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 5. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png |thumb|right|400px|Figure 2. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 5. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 3. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png |thumb|right|400px|Figure 3. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 6. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.<br />
<br />
<br />
= References =<br />
* Fredsoe, J. (1984). “Turbulent boundary layer in wave-current motion,” Journal of Hydraulic Engineering, ASCE, 110, 1103-1120.<br />
* Stive, M.J.F., and De Vriend, H.J. (1994). “Shear stress and mean flow in shoaling and breaking waves,” in Proceedings 24th International Coastal Engineering Conference, ASCE, New York, 594-608 pp.<br />
* Visser, R. J. (1991). “Laboratory measurements of uniform longshore currents”. Coastal Engineering, 15, 563-593.<br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10565Planar Beach2014-04-17T21:09:46Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 1.<br />
<br />
{|border="1"<br />
|+ Table 1. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 1) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 2<br />
and 3 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png |thumb|right|400px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 2. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 3. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 4. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 2. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 5. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png |thumb|right|400px|Figure 2. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 5. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 3. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png |thumb|right|400px|Figure 3. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 6. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.<br />
<br />
<br />
= References =<br />
* Lynch, D.R., and Gray, W.G. (1978). "Analytical solutions for computer flow model testing," J. Hydraulics Division, 104, 1409-28. <br />
<br />
----<br />
[[Test_Cases]]</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10564Planar Beach2014-04-17T21:07:10Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 1.<br />
<br />
{|border="1"<br />
|+ Table 1. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 1) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 2<br />
and 3 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png |thumb|right|400px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 2. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 3. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 4. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 2. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 5. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png |thumb|right|400px|Figure 2. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 5. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 3. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png |thumb|right|400px|Figure 3. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 6. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10563Planar Beach2014-04-17T21:06:19Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 1.<br />
<br />
{|border="1"<br />
|+ Table 1. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 1) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 2<br />
and 3 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png |thumb|right|600px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 2. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 3. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 4. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 2. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 5. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png |thumb|right|600px|Figure 2. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 5. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 3. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png |thumb|right|600px|Figure 3. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 6. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10562Planar Beach2014-04-17T21:03:39Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 21.<br />
<br />
{|border="1"<br />
|+ Table 1. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 22) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 22<br />
and 23 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png |thumb|right|600px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 2. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 3. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 4. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 23. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 25. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png |thumb|right|600px|Figure 2. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 5. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 24. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png |thumb|right|600px|Figure 3. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.]]<br />
<br />
<br />
<br />
{|border="1"<br />
|+ Table 6. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10561Planar Beach2014-04-17T21:00:56Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 21.<br />
<br />
{|border="1"<br />
|+ Table 21. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 22) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 22<br />
and 23 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png ||thumb|right|600px|Figure 1. CMS computational grid for the Visser (1991) test cases.]]<br />
<br />
<br />
{|border="1"<br />
|+ Table 22. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 23. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 24. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 23. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 25. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png ||leftthumb|400px|alt=framework]]<br />
Figure 23. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.<br />
<br />
<br />
{|border="1"<br />
|+ Table 25. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 24. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png ||leftthumb|400px|alt=framework]]<br />
Figure 24. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.<br />
<br />
<br />
{|border="1"<br />
|+ Table 26. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.</div>U4hcsdawhttps://cirpwiki.info/index.php?title=Planar_Beach&diff=10560Planar Beach2014-04-17T20:59:39Z<p>U4hcsdaw: </p>
<hr />
<div>Test C2-Ex3: Planar sloping beach with oblique incident regular waves<br />
<br />
= Purpose =<br />
<br />
The CMS is applied to a laboratory experiment of wave-induced currents<br />
and water levels due to regular waves. The large cross-shore gradient<br />
of wave height in the surf zone produces a large forcing useful for<br />
testing hydrodynamic model stability and performance under strong wave<br />
forcing. The specific CMS-Flow features tested are the surface roller,<br />
cross-shore boundary conditions, and combined wave-current bottom<br />
shear stress parameterization.<br />
<br />
<br />
= Experiment =<br />
<br />
In 1991, Visser conducted eight laboratory experiments of<br />
monochromatic waves on a planar beach and collected measurements on<br />
waves, currents and water levels. In this report, experiments (Cases)<br />
4 and 7 are selected as representative test cases. The bathymetry<br />
consisted of a 1:10 slope for the first 1 m from shore, a 1:20 slope<br />
for the next 5 m, followed by 5.9-m flat bottom to the wave<br />
generator. Cases 4 and 7 had an incident wave height of 0.078 m, peak<br />
period of 1.02 s and incident wave angle of 15.4°. Case 4 was run over<br />
a concrete bed and Case 7 was run over a thin 0.005-0.01 m layer of<br />
gravel grouted onto the concrete floor. A summary of the wave<br />
conditions is provided in Table 21.<br />
<br />
{|border="1"<br />
|+ Table 21. Wave conditions for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave height (regular) || 0.078 m<br />
|-<br />
|Wave period || 1.02 s<br />
|-<br />
|Incident wave angle || 15.4º<br />
|}<br />
<br />
= Model Setup =<br />
<br />
The computational grid (Figure 22) consists of 84 rows and 147 columns<br />
with a constant grid resolution in the longshore direction of 0.15 m<br />
and a variable grid resolution between 0.04 and 0.15 m in the<br />
cross-shore direction. A constant zero water level was forced at the<br />
offshore boundary and cross-shore boundaries were applied on each side<br />
of the shoreline. The boundary type solves the 1-D cross-shore<br />
momentum equations for the longshore current and water level and<br />
applies a flux boundary condition for inflow conditions and a water<br />
level condition for outflow conditions. The combined wave-current<br />
bottom shear stress model of Fredsoe (1984) is used. The cases were<br />
simulated as steady-state solutions with pseudo-time stepping to reach<br />
steady-state while coupling waves, currents and water levels. The<br />
initial condition was specified as zero current velocity and water<br />
level for the whole domain. Waves and hydrodynamics were coupled every<br />
20 min (steering interval) and run until steady-state. The surface<br />
roller model (Stive and De Vriend 1994)was run after each CMS-Wave run<br />
and the roller surface stresses were then added to the wave radiation<br />
stresses before running CMS-Flow. A summary of the important<br />
simulation settings for CMS-Flow and CMS-Wave is given in Tables 22<br />
and 23 respectively. The experiments was simulated in laboratory<br />
scale, which is why some of the parameters like the wetting/drying<br />
depth were decreased.<br />
<br />
<br />
[[File:Visser_test_grid.png ||leftthumb|400px|alt=framework]]<br />
Figure 22. CMS computational grid for the Visser (1991) test cases.<br />
<br />
{|border="1"<br />
|+ Table 22. CMS-Flow settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Solution scheme || Implicit<br />
|-<br />
|Time step || 1 min<br />
|-<br />
|Wetting/drying depth || 0.006 m<br />
|-<br />
|Simulation duration || 3 hr<br />
|-<br />
|Ramp duration || 2 hr<br />
|-<br />
|Wave-current bottom friction || Fredsoe (1984)<br />
|}<br />
<br />
{|border="1"<br />
|+ Table 23. CMS-Wave settings for the Visser (1991) test cases.<br />
!Parameter !! Value<br />
|-<br />
|Wave breaking formulation || Battjes and Janssen (1981)<br />
|-<br />
|Bottom friction || Off (default)<br />
|-<br />
|Steering interval || 20 min<br />
|}<br />
<br />
All of the wave breaking formulations in CMS-Wave are designed for<br />
random waves. However the Visser (1991) laboratory experiments were<br />
run with regular (monochromatic) waves which are not useful for<br />
validating the CMS-Wave. Since the objective of this test case was to<br />
assess the performance of the hydrodynamics, it was necessary to<br />
calibrate the waves to obtain the most accurate wave results in order<br />
to analyze the performance of the hydrodynamic model by itself and not<br />
have the analysis impacted by the results from an inadequately<br />
calibrated wave model. The calibration procedure consisted of first<br />
calibrating the location of the breaker using the breaker index γ. The<br />
flow was then calibrated using the Manning's coefficient and roller<br />
efficiency coefficient (Stive and De Vriend 1994). Additional tests<br />
were run for comparison with the same settings except the roller model<br />
was turned off.<br />
<br />
{|border="1"<br />
|+ Table 24. Calibration parameters for the Visser (1991) test cases.<br />
!Parameter !! Case 4 !! Case 7 !! Default<br />
|-<br />
|Manning’s coefficient,s/m1/3 (flow only) || 0.0115 || 0.018|| None<br />
|-<br />
|Breaker coefficient || 0.64 || 0.9 || Automatic(random waves)<br />
|-<br />
|Roller dissipation coefficient || 0.1 || 0.1 || 0.1<br />
|-<br />
|Roller efficiency factor || 0.8 || 0.8 || 1.0<br />
|}<br />
<br />
<br />
<br />
= Results and Discussion =<br />
<br />
<br />
''Case 4''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels for Case 4 are compared in Figure 23. Results are shown with<br />
and without the surface roller. The results are significantly improved<br />
when the surface roller is included as demonstrated by the<br />
goodness-of-fit statistics shown in Table 25. The NMAE for longshore<br />
current was reduced from approximately 20 to 5%. The roller has the<br />
effect of spreading the peak longshore current and moving it closer to<br />
the shore. The surface roller also reduces the setup at the breaker<br />
and increases it in the surf zone and near the shoreline. Although the<br />
water levels and currents are significantly affected by the surface<br />
roller the wave height profile shows only minor differences when the<br />
roller is included. This is due to the fact that in this case the<br />
dominant wave process in the surf zone is the wave breaking and the<br />
current-wave interaction is relatively weak in the wave model.<br />
<br />
[[File:Visser_Wave_Heights_Case4.png ||leftthumb|400px|alt=framework]]<br />
Figure 23. Measured and calculated wave height (top), longshore<br />
current (middle), and water level (bottom) for Visser (1991) Case 4.<br />
<br />
<br />
{|border="1"<br />
|+ Table 25. Goodness-of-fit statistics for the Visser (1991) Case 4.<br />
! !! !! NRMSE, % !!NMAE,%!!R2 !!Bias<br />
|-<br />
|No Roller|| Wave height || 7.10 || 5.35||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 22.59 || 19.91||0.609 ||0.018 m/s<br />
|-<br />
| || Water level || 13.95 || 11.66||0.954 ||0.000 m<br />
|-<br />
|Roller || Wave height || 6.70 || 5.11 ||0.985 ||0.002 m<br />
|-<br />
| || Longshore current || 7.14 || 5.11 ||0.962 ||0.007 m/s<br />
|-<br />
| || Water level || 9.04 || 7.38 ||0.957 ||0.000 m<br />
|}<br />
<br />
''Case 7''<br />
<br />
The measured and computed wave heights, longshore currents, and water<br />
levels with and without the roller for Case 7 are shown in<br />
Figure 24. It is interesting to note that although the offshore wave<br />
height, period and direction are the same as Case 4, the location of<br />
the breaker for Case 7 is significantly further offshore. It is<br />
suspected that Case 7 actually had a larger wave height than Case 4<br />
which produced a larger breaker further offshore. However, because no<br />
measurements were available further offshore of the breaker, no<br />
changes were made to the incident wave height. The results are similar<br />
to those of Case 4 in that the longshore current velocities are significantly improved when the roller is included (see Table 26). No<br />
measurements of water levels were available for Case 7. Similarly to<br />
Case 4 the longshore current is well predicted when the roller is<br />
included except for the first 1 m from the shoreline where the current<br />
velocity is overpredicted.<br />
<br />
<br />
[[File:Visser_Wave_Heights_Case7.png ||leftthumb|400px|alt=framework]]<br />
Figure 24. Measured and computed longshore currents (top), water<br />
levels (middle) and wave heights (bottom) for Visser (1991) Case 7.<br />
<br />
<br />
{|border="1"<br />
|+ Table 26. Goodness-of-fit statistics for the Visser (1991) Case 7.<br />
!!Roller!!Variable !!NRMSE, % !!NMAE, % !!<math>R^2</math>!!Bias<br />
|- <br />
|Off ||Wave height ||7.10 ||5.35 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||22.59 ||19.91 || 0.609 ||0.018 m/s<br />
|-<br />
| ||Water level ||13.95 ||11.66 || 0.954 ||0.000 m<br />
|-<br />
|On ||Wave height ||6.70 ||5.11 || 0.985 ||0.002 m<br />
|-<br />
| ||Longshore current||7.14 ||5.11 || 0.962 ||0.007 m/s<br />
|-<br />
| ||Water level ||9.04 ||7.38 || 0.957 ||0.000 m<br />
|}<br />
<br />
= Conclusions and Recommendations =<br />
<br />
Wave-induced currents and water levels were simulated with the CMS for<br />
the case of monochromatic waves over a planar bathymetry. Results were<br />
calculated with and without the surface roller and the best results<br />
were obtained with the roller turned on, using a roller dissipation<br />
coefficient of 0.1 and a roller efficiency factor of 0.8. Both<br />
currents and water levels were predicted with errors less than<br />
10%. Additional tests will be conducted in the future to show model<br />
sensitivity to the calibration parameters and to better determine<br />
these parameters based on field conditions. The wave calibration and<br />
results shown here are related to regular waves and are not directly<br />
applicable to field conditions. However, the purpose of these tests<br />
was to test the performance of the hydrodynamic model as quantified by<br />
the comparison between measured and simulated longshore current<br />
velocities and water levels under strong wave forcing.</div>U4hcsdaw