The Evolution of Nonlinear Wave Statistics through a Variable Medium

Abstract

n coastal areas and on beaches, nonlinear effects in ocean waves are dominated by so-called triad interactions. These effects can result in large energy transfers across the wave spectrum and result in non-Gaussian wave statistics, which is important for coastal wave propagation and wave-induced transport processes. To model these effects in a stochastic wave model based on the radiative transfer equation (RTE) requires a transport equation for three-wave correlators (the bispectrum) that is compatible with quasi-homogeneous theory. Based on methods developed in optics and quantum mechanics, the authors present a general approach to derive a transport equation for higher-order correlators. The principal result of this work is a coupled set of equations consisting of the radiative transfer equation with a nonlinear forcing term and a new, generalized transport equation for bispectrum. This study discusses the implications and characteristics of the resulting equations and shows that the model contains various shallow- and deep-water asymptotes for nonlinear wave propagation as special cases.