From deep to shallow water 2D wave turbulence: Emergence of soliton gas

Abstract: Experiments on 2D random water wave propagation in a large wave tank are analyzed when the effect of dispersion changes. A stereoscopic profilometry technique is used to measure the water surface displacement resolved in both time and space over a significant fraction of the wave tank. The wave regimes are characterized by analyzing the space-time spectral statistical properties of the wave field. At a given, finite, water depth, the effect of dispersion can be varied by tuning the peak frequency of the wave generation. In shallow water conditions, the waves are only weakly dispersive and this enables the propagation of solitons. {In these conditions random wave forcing produces soliton gases}. In deep water conditions, the waves are dispersive and for wideband spectra, one observes the development of weak turbulence. A transition between these regimes is observed when changing the peak forcing frequency (dispersion) and the wave amplitude (nonlinearity), with a clear threshold between states with solitons and soliton-less states. The development of a soliton gas is associated with a strong change of the wave spectrum as well as a significant evolution of the distribution of the water elevation. We also observed a strong effect of the finite size of the tank due to the peculiar reflection laws of line solitons.