On Deviations from Gaussian Statistics for Surface Gravity Waves

TL;DR

This paper explores how deviations from Gaussian statistics in ocean surface waves can be modeled using weak turbulence theory, highlighting the roles of bound and free modes and deriving formulas for skewness and kurtosis.

Contribution

It introduces a framework to incorporate non-Gaussian deviations in surface wave statistics through weak turbulence theory, including explicit formulas for skewness and kurtosis.

Findings

Deviations from Gaussian statistics can be naturally modeled using weak turbulence theory.

Bound and free modes significantly influence surface elevation statistics.

Derived formulas relate skewness and kurtosis to spectral wave action density.

Abstract

Here we discuss some issues concerning the statistical properties of ocean surface waves. We show that, using the approach of weak turbulence theory, deviations from Gaussian statistics can be naturally included. In particular we discuss the role of bound and free modes for the determination of the statistical properties of the surface elevation. General formulas for skewness and kurtosis as a function of the spectral wave action density are here derived.