Effects of strong turbulence for water waves

TL;DR

This paper presents direct numerical simulations of water wave turbulence, revealing that strong turbulence involves wave breaking, cusp formation, and intermittency, with spectra following a -4 power law, challenging the weak turbulence regime.

Contribution

It introduces a model capturing strong turbulence effects in water waves, including wave breaking and cusp formation, not observed in weak turbulence theories.

Findings

Wave spectra follow a -4 power law in frequency and wavenumber.

Wave breaking and cusp formation dominate the turbulence dynamics.

Probability density of wave steepness exhibits power-law tails, indicating intermittency.

Abstract

The results of direct numerical simulation of plane-symmetric turbulence of water waves for potential flows within the framework of conformal variables taking into account low-frequency pumping and high-frequency viscous dissipation are presented. In this model, for a wide range of pumping amplitudes, the weak turbulence regime was not detected. It is shown that for typical turbulence parameters, the main effects are the processes of wave breaking, the formation of cusps on wave crests, which make the main contribution to the turbulence spectra with a dependence on frequency and wavenumber with the same exponent equal to $-4$. In this strongly nonlinear regime, the probability density of wave steepness at large deviations has power-law tails responsible for the intermittency of turbulence.