From dispersive wave turbulence to an acoustic-like wave regime

Wave turbulence is a statistical state in which numerous random weakly nonlinear waves interact with each other. It leads to an energy cascade from large scales down to small scales driven by resonant interactions between waves. This state is first evidenced experimentally in a one dimensional canal for dispersive gravity-capillary waves on the surface of mercury [1]. Then by using a ferrofluid and a high external magnetic field, we managed to experimentally create a transition from dispersive wave turbulence to a nondispersive regime involving coherent structures which are found to be shock waves [2]. These structures are characterized by a significant steepening with a discontinuity, and correspond to singularities in their second order derivative. Because of the discontinuities, shock waves then transfer energy at every scales instantly and become thus the main process to cascade energy over scales.

[1] G. Ricard, and E. Falcon, Experimental quasi-1D capillary-wave turbulence, EPL, 135, 64001 (2021).

[2] G. Ricard, and E. Falcon, From dispersive wave turbulence to an acoustic-like wave regime, planned paper.