SPECTRAL MODELING OF WAVE BREAKING - APPLICATION TO BOUSSINESQ EQUATIONS

The nonlinear transformation of wave spectra in shallow water is consi dered, in particular, the role of wave breaking and the energy transfe r among spectral components due to triad interactions. Energy dissipat ion due to wave breaking is formulated in a spectral form, both for en ergy-density models and complex-amplitude models. The spectral breakin g function distributes the total rate of random-wave energy dissipatio n in proportion to the local spectral level, based on experimental res ults obtained for single-peaked spectra that breaking does not appear to alter the spectral shape significantly. The spectral breaking term is incorporated in a set of coupled evolution equations for complex Fo urier amplitudes, based on ideal-fluid Boussinesq equations for wave m otion. The model is used to predict the surface elevations from given complex Fourier amplitudes obtained from measured time records in labo ratory experiments at the upwave boundary. The model is also used, tog ether with the assumption of random, independent initial phases, to ca lculate the evolution of the energy spectrum of random waves. The resu lts show encouraging agreement with observed surface elevations as wel l as spectra.