3-wave and 4-wave interactions in gravity wave turbulence

The Weak Turbulence Theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We setup an isotropic state of interacting gravity waves in the Coriolis facility (13~m diameter circular wave tank) by exciting waves at 1~Hz by wedge wavemakers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved both in space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and than the field observations in the Black Sea by Leckler {\it et al. JPO} 2015. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wavevector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler {\it et al.} for comparison with the laboratory data. 3-wave coupling are characterized and shown to involve mostly quasi resonances of waves with second or higher order harmonics. 4-wave coupling are not observed in the laboratory but are evidenced in the field data. We finally discuss temporal scale separation to explain our observations.