Long wave propagation: Difference between revisions

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= Analytical Solution =
= Problem =
The purpose of this verification test is to assess the model performance in simulating long wave propagation. The case is also useful for testing the model performance and symmetry for a non-rectangular domain. The test case consists of a quarter annulus with a linear bed elevation in the radial direction. The inner radius is 60.96 km (200,000 ft), and the outer radius is 152.4 km (500,000 ft). The analytical is given by Lynch and Gray (1978).  
Lynch and Gray (1978) presented the analytical solution for depth-averaged long-wave propagation in am annular domain. Here the case tested with a linearly sloping bed, and without bottom friction, Coriolis, or horizontal mixing. The offshore boundary consists of an single tidal constituent. Table 1 summarizes the important model settings used for this test.  


'''Table 1. General Settings for Flow over a Bump'''
'''Table 1. General Settings for quarter annulus test'''
{|border="1"
{|border="1"
|'''Parameter''' ||'''Value'''
|'''Parameter''' ||'''Value'''
|-
|-
|Deepwater Tidal Amplitude|| 0.3048 m
|Deepwater tidal amplitude|| 0.3048 m
|-
|-
|Tidal Period || 12.42 hrs (M2)
|Tidal period || 12.42 hrs (M2)
|-
|Inner radius || 60.96 km
|-
|Outer radius || 152.4 km
|-
|Depth at inner radius || 10.02 m
|-
|Depth at outher || 25.05 m
|-
|-
|Bottom  friction || None
|Bottom  friction || None
|-
|-
|Horizontal eddy viscosity || None
|Horizontal eddy viscosity || 0.0
|-
|Corilis || 0.0
|}
|}


Revision as of 23:10, 1 June 2011

Problem

Lynch and Gray (1978) presented the analytical solution for depth-averaged long-wave propagation in am annular domain. Here the case tested with a linearly sloping bed, and without bottom friction, Coriolis, or horizontal mixing. The offshore boundary consists of an single tidal constituent. Table 1 summarizes the important model settings used for this test.

Table 1. General Settings for quarter annulus test

Parameter Value
Deepwater tidal amplitude 0.3048 m
Tidal period 12.42 hrs (M2)
Inner radius 60.96 km
Outer radius 152.4 km
Depth at inner radius 10.02 m
Depth at outher 25.05 m
Bottom friction None
Horizontal eddy viscosity 0.0
Corilis 0.0

Model Setup

Figure 1. Quarter Annulus

A Cartesian grid is used with two levels of refinement. The computational grid is shown in Figure 1. The general model settings are shown in Table 2.

Table 2. General Settings for Flow over a Bump

Parameter Value
Time step 600 sec (10 min)
Ramp period 24 hrs
Simulation time 120 hrs
Grid resolution 2-8 km
Number of active ocean cells 1160
Wall friction Off


Results

The figure below shows a time series of water levels at the inner edge of the model domain. The goodness of fit statistics are listed in the below. The model accurately predicts the wave phase but slightly overestimates the amplitude by approximately 0.01 m.

Table 3. Goodness of fit statistics for the water elevation

Statistic Value
RMSE 0.014 m
RMAE 0.028
R^2 0.999
Bias 0.003 m

QA Water Level 8km.png


References

  • Lynch, D.R., and Gray, W.G. (1978). "Analytical solutions for computer flow model testing," J. Hydraulics Division, 104, 1409-28.

Test_Cases

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