MODELING SPECTRA OF BREAKING SURFACE-WAVES IN SHALLOW-WATER

Predictions from Boussinesq-equation-based models for the evolution of breaking surface gravity waves in shallow water are compared with fie ld and laboratory observations. In the majority of the 10 cases invest igated, the observed spectral evolution across the surf zone is modele d more accurately by a dissipation that increases at high frequency th an by a frequency-independent dissipation. However, in each case the p redicted spectra are qualitatively accurate for a wide range of freque ncy-dependent dissipations, apparently because preferential reduction of high-frequency energy (by dissipation that increases with increasin g frequency) is largely compensated by increased nonlinear energy tran sfers to high frequencies. In contrast to the insensitivity of predict ed spectral levels, model predictions of skewness and asymmetry (stati stical measures of the wave shapes) are sensitive to the frequency dep endence of the dissipation. The observed spatial evolution of skewness and asymmetry is predicted qualitatively well by the model with frequ ency-dependent dissipation, but ij predicted poorly with frequency-ind ependent dissipation. Although the extension of the Boussinesq equatio ns to breaking waves is ad hoc, a dissipation depending on the frequen cy squared (as previously suggested) reproduces well the observed evol ution of wave frequency spectra, skewness, and asymmetry.