conservation models with a depth-limited breaking criterion and simpler tech-

niques such as shoaling the component wave systems independently of each

other and superimposing the results. None of these techniques could reproduce

the observed changes to the wave spectrum.

Boussinesq model simulations were carried out for test case 7 in the Smith

and Vincent experiments. The sea state is composed of two irregular wave

components described by TMA spectra with *H*mo,1 = 7.6 cm, *T*p,1 = 2.5 s, *H*mo,2 =

13.2 cm, *T*p,1 = 1.75 s, and γ = 20. The numerical wave flume is 41 m long and

consists of a 20-m-long constant-depth region and a 1:30 planar beach. The water

depth in the constant depth section of the flume was 0.61 m. The measured time

series at the offshore gauge was used to generate velocity boundary conditions

for the numerical model. A grid spacing of 0.125 m and time-step size of 0.04 s

was used for the numerical simulations.

Figures 19 to 22 show comparisons of the measured and predicted wave

spectra at gauges located in water depths of 61 cm, 18.3 cm, 9.1 cm, and 6.1 cm.

Although the higher frequency component dominates the incident wave spectrum

with 67 percent of the wave energy at *h *= 61 cm, its energy is preferentially dis-

sipated with the lower frequency component becoming dominant at the shallow

depth of 6.1 cm. The Boussinesq model is able to reproduce the observed trends

in the experimental data. The primary reason for the preferential reduction in

energy of the high-frequency component is due to the nonlinear cross-spectral

transfer of energy during the shoaling process.

Water Depth = 61cm

0.01

Measured

Predicted

0.008

0.006

0.004

0.002

0

0

0.5

1

1.5

2

Frequency (Hz)

Figure 19. Measured and predicted wave spectra at Gauge 1 for bimodal sea

state shoaling on a constant slope beach

49

Chapter 5 Model Validation

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