Direct numerical simulations of capillary wave turbulence

TL;DR

This paper uses direct numerical simulations to study capillary wave turbulence, confirming the weak turbulence theory's predictions about wave spectra, energy flux, and time scale separation in a two-phase flow system.

Contribution

It provides the first comprehensive 3D numerical validation of weak turbulence theory for capillary waves, including spectral laws and energy flux estimates.

Findings

Wave height spectrum follows a power law consistent with theory

Kolmogorov-Zakharov constant matches theoretical predictions

Time scale separation observed between linear, nonlinear, and dissipative processes

Abstract

This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency in good agreement with weak turbulence theory. By estimating the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction and dissipative times is also observed. These numerical results confirm the validity of weak turbulence approach to quantify out-of equilibrium wave statistics.