directional spreading of wave energy leads to larger wave heights in the sheltered
area behind the breakwaters and smaller wave heights along the principal direc
tion of the waves.
Multidirectional Wave Propagation over a Shoal
Laboratory experiments on the transformation of irregular multidirectional
waves over an elliptical shoal were carried out by Vincent and Briggs (1989).
The experimental layout is shown in Figure 12, and consists of an elliptical shoal
placed in a 0.4572mdeep basin. The boundary of the shoal is an ellipse defined
by:
2
2
x  xc
y  yc
+
=1
(64)
3.96
3.05
where (xc, yc ) are the coordinates of the center of the shoal and are given by xc =
13.72 m and yc = 6.10 m. The water depth over the shoal is given by:
0.5
y  yc
2
2
x  xc
h( x, y ) = 0.9144  0.7620 1 

(65)
4.95
3.81
The minimum water depth over the shoal is 0.1524 m. Tests were carried out
for various regular and irregular, unidirectional and multidirectional waves. For
irregular waves, the TMA spectrum was used to describe the frequency distribu
tion of wave energy, while the wrappednormal distribution was used for the
directional spreading function. Watersurface elevation data were collected at
five transects located at distances of 3.05 m, 6.10 m, 9.14 m, 12.19 m, and
15.24 m from the wavemaker as shown in Figure 12.
The numerical basin for the BOUSS2D model simulations is 31.5 m wide,
27 m long, with a uniform grid spacing of 0.1 m. Twometerwide damping
layers were placed around the perimeter of the basin to absorb outgoing waves.
Two representative test cases were selected for the modeldata comparisons. Test
case N1 is characterized by a TMA spectrum with significant wave height Hmo =
0.0775 m, peak period Tp = 1.3 s, peak enhancement factor γ = 2, and a narrow
directional distribution with standard deviation σθ = 10 deg. Test case B1 is
characterized by a TMA spectrum with significant wave height Hmo = 0.0775 m,
peak period Tp = 1.3 s, peak enhancement factor γ = 2, and a broad directional
distribution with standard deviation σθ = 30 deg. Timehistories of the velocity
boundary conditions along the wavemaker were synthesized for a duration of
130 s, corresponding to 100 wave periods. Simulations were carried out using a
timestep size ∆t = 0.025 s.
44
Chapter 5 Model Validation