Experimental study of integrable turbulence in shallow water

Abstract

We analyze a set of bidirectional wave experiments in a linear wave flume of which some are conducive to integrable turbulence. In all experiments the wavemaker forcing is sinusoidal and the wave motion is recorded by seven high-resolution side-looking cameras. The periodic scattering transform is implemented and power spectral densities computed to discriminate linear wave motion states from integrable turbulence and soliton gas. Values of the wavemaker forcing Ursell number and relative amplitude are required to be above some threshold values for the integral turbulence to occur. Despite the unavoidable slow damping, soliton gases achieve stationary states because of the continuous energy input by the wavemaker. The statistical properties are given in terms of probability density distribution, skewness and kurtosis. The route to integrable turbulence, by the disorganization of the wavemaker induced sinusoidal wave motion, depends on the non-linearity of the waves but equally on the amplitude amplification and reduction due to the wavemaker feedback on the wave field.