Effects of coherent dynamics of stochastic deep-water waves

TL;DR

This paper introduces a spectral filtering method to analyze nonlinear wave components in deep-water waves, revealing that free wave dynamics significantly influence surface displacement kurtosis and exhibit non-Gaussian behavior with coherent patterns.

Contribution

A novel spectral filtering technique is developed to separate nonlinear wave components and analyze free wave dynamics in realistic sea states.

Findings

Free wave surface displacement kurtosis is significantly affected by free wave dynamics.

Coherent wave patterns form 'jets' in Fourier space, violating classic dispersion relations.

Surface displacement kurtosis can be explained by the non-Gaussian behavior of free waves.

Abstract

A method of windowed spatio-temporal spectral filtering is proposed to segregate different nonlinear wave components, and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able to contribute essentially to the abnormally large values of the surface displacement kurtosis, according to the direct numerical simulations of realistic sea waves. In this situation the free wave stochastic dynamics is strongly non-Gaussian, and the kinetic approach is inapplicable. Traces of coherent wave patterns are found in the Fourier transform of the directional irregular sea waves; they may form 'jets' in the Fourier domain which strongly violate the classic dispersion relation.