Numerical simulation of surface waves instability on a discrete grid

TL;DR

This paper presents comprehensive numerical simulations of surface wave instabilities on deep fluids, revealing how weakly nonlinear waves evolve into chaotic turbulence through different wave interaction mechanisms.

Contribution

It introduces a detailed numerical algorithm for simulating wave instabilities, covering both capillary and gravity waves, with theoretical analysis included.

Findings

Instability leads to wave chaotization and turbulence.

Different wave interactions cause distinct instability behaviors.

Numerical results align with theoretical predictions.

Abstract

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of propagating and standing waves. We studied separately pure capillary wave unstable due to three-wave interactions and pure gravity waves unstable due to four-wave interactions. The theoretical description of instabilities in all cases is included into the article. The numerical algorithm used in these and many other previous simulations performed by authors is described in details.