Turbulence of capillary waves forced by steep gravity waves

TL;DR

This study experimentally investigates the turbulence and statistical properties of capillary waves driven by steep gravity waves, revealing power-law spectra and complex energy transfer mechanisms that challenge existing wave turbulence theories.

Contribution

It provides new experimental insights into the nonlinear dynamics of capillary waves under steep gravity wave forcing, highlighting the need for extended theoretical models.

Findings

Power-law spectra observed in space and time for steep gravity waves.

Spectral fluctuations result from intermittent nonlinear events.

Wave spectrum exponents align with weakly nonlinear Wave Turbulence Theory.

Abstract

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free-surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness ($0.2-0.3$), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from large scale to small scale. Analysis of temporal fluctuations of spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of wave spectrum are found to be in agreement with those of the weakly nonlinear Wave Turbulence Theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with Wave Turbulence Theory. These results suggest that theoretical developments beyond the classic Wave Turbulence Theory are necessary to describe the dynamics and statistics of capillary waves in natural environment. In particular, in presence of broad scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions could be reconsidered.