Nonlocal resonances in weak turbulence of gravity-capillary waves

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.