A spectral model for unidirectional nonlinear wave propagation over arbitrary depths

Abstract

A weakly-nonlinear and dispersive wave equation recently developed by the authors is used for formulating a spectral-type unidirectional wave propagation model describing spectral transformations of narrow-band waves travelling over arbitrary depths. The essential characteristics of the model equation are recapitulated first and then the spectral domain representation in terms of spatially varying harmonic amplitudes is presented. The resulting evolution equations are used to simulate the experiments concerning harmonic generation in shallow water and nonlinear random wave transformations over a submerged bar. Furthermore, the spectral model predictions are compared with the field measurements in nearshore with satisfactory results.