A 2-D Random Wave Transformation Model with Gradational Breaker Index

Random wave transformations with breaking in shallow water of 2-D bathymetry are computed with the parabolic equation. A new system of gradational breaker index, the value of which gradually decreases as the level of wave height within a wave group is lowered, is introduced to simulate gradual shape variations of wave height distribution in the surf zone. Wave attenuation in the trough area of a barred beach is treated with a secondary gradational breaker index, which is applied for locations in water of constant or increasing depth. Its empirical coefficients are assigned values different from those in water of decreasing depth. The wave attenuation factor due to bottom friction is formulated by evaluating the rate of energy dissipation by shear stress along the sea bottom. Computation is made for directional spectral components with multiple levels of wave heights under the Rayleigh distribution, and the results are synthesized for the calculation of wave height distributions. The new computational scheme succeeds in reproducing the random wave breaking diagrams by Goda (1975), and shows good agreements with several experimental results on wave transformations over horizontal shelves, barred beaches, and an elliptical shoal. The scheme also yields wave height predictions in good agreement with several field measurements across the surf zone.

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