Ocean swell within the kinetic equation for water waves

TL;DR

This paper investigates how wave-wave interactions influence ocean swell evolution using extensive simulations of the kinetic Hasselmann equation, revealing self-similarity, energy drops, and universal spectral features over long timescales.

Contribution

It demonstrates the relevance of Kolmogorov-Zakharov solutions to swell evolution and details the impact of wave interactions on spectral self-similarity and energy dissipation.

Findings

Pronounced wave energy drop at initial stages (~1000 km scale)

Universal angular distribution of spectra at long times

Self-similar wave spectral features identified

Abstract

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.