Identifying four wave resonant interactions in a surface gravity wave turbulence experiment.

The nonlinear dynamics of waves at the sea surface is believed to be ruled by the Weak Turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility, which is a 13-meter diameter circular tank. An isotropic and statistically stationary wave turbulence of average steepness of 10% is maintained by two wedge wave makers. The space and time resolved wave elevation is measured using a stereoscopic technique. Wave-wave interactions are analyzed through third and fourth order correlations. We specifically focus on the role of bound waves generated by non-resonant 3-wave coupling. We implement a space-time filter to separate the dynamics of free waves from the bound waves, observing that the free wave dynamics leads to weak resonant 4-wave correlations. This weak level of correlation is foundational to the Weak Turbulence Theory, thus supporting its application in modeling gravity wave turbulence as seen in current operational wave forecasting models. Although theory suggests bound waves do not contribute to energy cascade, our findings raise questions about their impact on dissipation and energy transfers.