small wave height radiating away from the shoal in the down-wave direction that are not

present in the lab data. The model results in Figure 15 do not show the same level of

modulation as the lab results. The N1 solutions, although not shown, exhibit the same

down wave characteristics as the B1 solutions.

The numerical solution approaches the lab data when the directional resolution is

increased. Figures 16 and 17 show the results for the B1 and N1 spectra, respectively,

using ∆θ equal to 4.14 The widths of the directional spectra were limited to +/- 60for

.

B1 and +/-30for N1 spectra, since negligible amounts of energy are outside this range.

The finger like patterns found in the cases with large ∆θ were not seen in these results.

This finding agrees with the observations made by Zhao and Anastasiou (1993) and

Panchang et al. (1990) regarding the width of directional bins needed in the input spectra.

The effect of amplitude-dependent non-linear dispersion was examined for the B1

and N1 cases.

Zhao and Anastasiou (1993)show an improvement in the numerical

solution. The CGWAVE results are essentially unchanged (Figures 16 and 17). This

occurs because CGWAVE operates on each spectral component independently. Once a

linear solution for a given component is found, these solution amplitudes are used in the

non-linear dispersion relation and the new solution is found. The new amplitudes are

again used in the non-linear mechanism. These iterations continue until a convergence

criterion is reached. The final solution to the component is saved and the model is run for

the next component. The incident wave heights associated with each spectral component

are, at their largest, an order of magnitude smaller than the significant wave height. The

wave heights used to compute non-linear effects are only a fraction of the significant wave

height, causing the non-linear dispersion relation to have a negligible effect.

For this problem, CGWAVE produces linear results that closely match the data for

the monochromatic waves propagating over the shoal.

The inclusion of wave-wave

interaction has improved the quality of this solution. CGWAVE also produces linear

results that closely match the data for the irregular wave cases when adequate directional

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