A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part I: Theoretical Development

Abstract

A new method for estimating the transfer rates in wind wave spectra is derived and tested, based on a two-scale approximation (TSA) to the total integral for quadruplet wave?wave interactions. Comparisons of this new estimation method to the full integral are given for several idealized spectra, including Joint North Sea Wave Project spectra with different peakednesses, a finite depth case, and cases with perturbations added to underlying parametric spectra. In particular, these comparisons show that the TSA is a significant improvement over the discrete interaction approximation (DIA) in deep water and an even greater improvement in shallow water.