Modeling spectra of breaking waves propagating over a beach

The spectral evolution of waves in shallow water is considered, in particular, wave breaking and the generation of sub- and super-harmonics. Modeling of these processes is based on a set of deterministic evolution equations for the propagation of fully dispersive nonlinear waves. Energy dissipation due to wave breaking is formulated in a spectral form and incorporated in the model. Previous laboratory measurements for wave transformation and breaking over barred and nonbarred beaches were compared against the model results. In order to obtain wave field statistics, Monte Carlo simulations are performed by assuming the wave field Gaussian at the upwave boundary. Modal amplitudes are derived from the observed density spectrum together with the assumption of random independent initial phases. The overall statistical parameters such as the significant wave height, mean wave period and skewness are determined. The overall model results show agreement with the measurements including the generation of low-frequency waves.