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

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. The lack of coherence is consistent with the lack of inverse cascade. At the highest frequencies, the very large values of the tricoherence are most likely due to a distinct 3-wave resonant process reported previously near the gravity-capillary crossover. As this process should be always operating, the condition for a clearer evidence of the 4-wave resonant process among gravity waves would require the use of a much larger wave facility.