Turbulence of capillary waves revisited

TL;DR

This paper revisits the turbulence of capillary waves, demonstrating that four-wave interactions are more relevant than the traditionally assumed three-wave interactions, leading to different energy spectrum exponents.

Contribution

It challenges the classical three-wave interaction model for capillary wave turbulence and highlights the importance of four-wave interactions in determining the energy spectrum.

Findings

Four-wave interactions lead to different spectral exponents.

Three-wave regime assumptions are often not fulfilled.

Higher order resonances can dominate in general dispersion scenarios.

Abstract

Kinetic regime of capillary wave turbulence is classically regarded in terms of three-wave interactions with the exponent of power energy spectrum being $\nu=-7/4$ (two-dimensional case). We show that a number of assumptions necessary for this regime to occur can not be fulfilled. Four-wave interactions of capillary waves should be taken into account instead, which leads to exponents $\nu=-13/6$ and $\nu=-3/2$ for one- and two-dimensional wavevectors correspondingly. It follows that for general dispersion functions of decay type, three-wave kinetic regime need not prevail and higher order resonances may play a major role. Accepted for publication.