Spectral modeling of unidirectional nonlinear wave propagation over arbitrary depths

A weakly-nonlinear and dispersive wave equation recently developed by the authors (Beji and Nadaoka, 1997) is used for formulating a spectral wave model describing transformations of narrow-banded unidirectional waves travelling over variable bathymetry. The performance of the model is tested against the measured data for harmonic generation over constant depth as well as nonlinear random wave propagation over varying depth. The comparisons indicate good agreement with the measurements and establish the reliability of the model. In closing, a semi-empirical dissipation term is formulated for simulating the energy loss due to breaking waves.