Effects of finite non-gaussianity on evolution of a random wind wave field

TL;DR

This study compares the long-term evolution of a random wind wave field using kinetic equations and direct numerical simulations, highlighting the impact of non-Gaussianity on spectral shape discrepancies.

Contribution

It demonstrates how non-Gaussian effects influence wave spectral evolution and clarifies the limitations of kinetic equations in modeling real wave fields.

Findings

DNS spectral shape aligns better with field observations.

Discrepancies are due to neglect of non-Gaussianity in kinetic models.

Spectral shape approaches kinetic predictions when nonlinear interactions diminish.

Abstract

We examine long-term evolution of a random wind wave field generated by constant forcing, by comparing numerical simulations of the kinetic equation and direct numerical simulations (DNS) of the dynamical equations. While integral characteristics of spectra are in reasonably good agreement, the spectral shapes differ considerably at large times, the DNS spectral shape being in much better agreement with field observations. Varying the number of resonant and approximately resonant wave interactions in the DNS numerical scheme, we show that when the ratio of nonlinear and linear parts of the Hamiltonian tends to zero, the DNS spectral shape approaches the shape predicted by the kinetic equation. We attribute the discrepancies between the kinetic equation modelling, on one side, and the DNS and observations, on the other, to the neglect of non-gaussianity in the derivation of the kinetic equation.