Modelling of nonlinear shoaling based on stochastic evolution equations

摘要

A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub-and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics are recast into evolution equations for the complex amplitudes. And serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing he well-known Gaussian closure hypothesis, nonlinear evolution equa- tions for the power spectrum and bispectrum are derived.