Spectral Modeling of Unidirectional Nonlinear Wave Propagation Over Arbitrary Depths Available to Purchase

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 traveling 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. I. Introduction Recent years have witnessed a constantly increasing interest towards the modeling of the nonlinear aspects of ocean waves. The trend originated from the need to explain definite obser"~ations which could not be accounted for by linear models. Wave skewness related sediment transport, influence of breaking on the surf-zone processes, and effects of harmonic generation on the characteristics of a wave field are the most striking examples of such phenomena (Doering and Bowen, 1986; Nadaoka et al., 1989; Kojima et al., 1990). For practical applications the nonlinear wave models are not yet in common use, however, there are evidences that when augmented with appropriate generation and dissipation mechanisms, these models may well be the prototypes of the commercial models to come. In this work a spectral model is developed using the recently introduced wave equation of Beji and Nadaoka (1997). The derivation is based on a Fourier series representation of the surface elevation with spatially varying amplitudes and phases. The resulting evolution equations are numerically solved for various test cases to demonstrate the capabilities of the model. Also, a semiemprical dissipation term is formulated to represent energy loss due to wave breaking.