Visser

Experimental Setup

In 1991, Visser conducted eight laboratory experiments of monochromatic wave on a planar beach and collected measurements on waves, currents and water levels. The bathymetry consisted of a 1:10 slope for the first 1-m seaward distance, a 1:20 slope for the next 5-m distance, followed by a 5.9 m distance of flat bottom to the wave generator. Both experiments had incident wave heights of 0.078 m, peak periods of 1.02 sec and an incident wave angle of 15.4°. Experiment 4 was run over a concrete bed and experiment 7 was run of a thin 0.005-0.01 m layer of gravel grouted on the concrete floor.

Table 1. Experiment Regular Wave Conditions

Parameter	Value
Height, m	0.08
Period, sec	1.02 m
Incident Angle,°	15.4

Model Setup

Computational Grid

The computational grid (shown in Figure 1) consists of 84 rows and 147 columns with a constant grid resolution in the longshore direction of 0.15 and a variable grid resolution between 0.04 and 0.15 m in the cross-shore direction. A zero water level was forced at the offshore boundary. A summary of some of the simulation settings used for both experiment cases are shown in the tables below.

Table 2. CMS-Flow Settings

Settings	Value
Solution scheme	Implicit
Time Step	60 sec
Wetting and Drying Depth	0.006 m
Simulation Duration	3 hr
Ramp Duration	3 hr
Wave-current bottom friction	Fredsoe 1984

Table 3. CMS-Wave Settings

Settings	Value
Wave Breaking	Battjes and Janssen
Bottom friction	Off
Steering Interval	0.25 hr
Surface Roller	On

Results

The calibration procedure consisted of first matching the wave profile by calibrating the location of the breaking wave height using the breaker index $\gamma$. The flow was then calibrated using the Manning's n coefficient and roller efficiency coefficient. The combined wave-current bottom friction was calculated based on Fredsoe 1984. Although this is not the default in CMS, it was choosen because of its strong theoritical backgroud compared to the default quadratic formula. Additional tests were run for comparison with the same settings except the roller model was turned off.

Table 4. Calibration Parameters

Calibration Parameters	Case 4	Case 7	Default
Breaker coefficient	0.64	0.9	0.73
Manning's n	0.0115	0.018	0.025
Roller efficiency coefficient	0.8	0.8	1.0

Figure 1. Comparison of measured wave height, water levels and longshore currents for Visser Case 4.

Figure 2. Comparison of measured wave height and longshore currents for Visser Case 7 (Note: No water level measurements are available for this case).

The goodness of fit statistics for both cases are shown in the table below

Table 5. Goodness of fit statistics

Statistic	Case 4				Case 7
	Wave Height, m	Longshore Current, m	Water level, m	Wave Height, m	Longshore Current, m
RMSE	0.0058	0.0289	0.030	0.0093	0.0186
RMAE	0.0305	0.0172	0.006	0.0359	0.0649
R^2	0.992	0.981	0.980	0.999	0.982

• For a definition of the goodness of fit statistics see Goodness of fit statistics

References

• Visser, R. J. (1991) “Laboratory measurements of uniform longshore currents”. Coastal Engineering, 15, 563-593.

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