Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

TL;DR

This study experimentally investigates gravity-capillary wave turbulence on a fluid surface, revealing localized energy branches, nonlinear dispersion relations, and scaling laws that challenge purely resonant interaction models.

Contribution

It provides the first detailed experimental measurement of the nonlinear dispersion relation and spatial statistics in wave turbulence, highlighting non-resonant energy transfer mechanisms.

Findings

Wave energy is localized on multiple branches in wave-vector-frequency space.

The nonlinear dispersion relation follows a specific power law.

Spatial spectra and amplitude distributions align with theoretical predictions.

Abstract

We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depend on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are not only restricted to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.