# The energy cascade of surface wave turbulence: toward identifying the active wave coupling

## TL;DR

This study experimentally investigates surface wave turbulence, revealing weak nonlinear interactions and the absence of an inverse cascade, challenging some theoretical predictions about wave energy transfer.

## Contribution

The paper provides experimental evidence on the nature of wave interactions, specifically showing weak 4-wave coupling and the lack of inverse cascade in surface wave turbulence.

## Key findings

- Weak 4-wave coupling observed via tricoherence analysis
- No evidence of inverse cascade in the experimental data
- Water deformation comprises linear waves and bound waves from non-resonant interactions

## Abstract

We investigate experimentally turbulence of surface gravity waves in the Coriolis facility in Grenoble by using both high sensitivity local probes and a time and space resolved stereoscopic reconstruction of the water surface. We show that the water deformation is made of the superposition of weakly nonlinear waves following the linear dispersion relation and of bound waves resulting from non resonant triadic interaction. Although the theory predicts a 4-wave resonant coupling supporting the presence of an inverse cascade of wave action, we do not observe such inverse cascade. We investigate 4-wave coupling by computing the tricoherence i.e. 4-wave correlations. We observed very weak values of the tricoherence at the frequencies excited on the linear dispersion relation that are consistent with the hypothesis of weak coupling underlying the weak turbulence theory.