Nonlocal resonances in weak turbulence of gravity-capillary waves

TL;DR

This study investigates weak turbulence in water surface waves near the gravity-capillary crossover, revealing that 3-wave resonant interactions are predominantly 1D and involve collinear wave vectors, with implications for oceanic wave dynamics.

Contribution

It demonstrates that nonlinear interactions in weak turbulence are mainly collinear and 1D, and highlights the role of nonlocal interactions between gravity and capillary waves.

Findings

Nonlinear processes involve 3-wave resonant interactions.

Interactions are predominantly 1D with collinear wave vectors.

Nonlocal interactions between gravity and capillary waves are possible.

Abstract

We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve 3-wave resonant interactions. By studying the solutions of the resonance conditions we show that the nonlinear interaction is dominantly 1D and involves collinear wave vectors. Furthermore taking into account the spectral widening due to weak nonlinearity explains that nonlocal interactions are possible between a gravity wave and high frequency capillary ones. We observe also that nonlinear 3-wave coupling is possible among gravity waves and we raise the question of the relevance of this mechanism for oceanic waves.