  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.
