Transition from wave turbulence to acousticlike shock-wave regime

TL;DR

This paper experimentally observes a transition from dispersive wave turbulence to shock waves on a fluid surface, showing how magnetic fields can control this transition and analyzing the resulting shock statistics and spectra.

Contribution

It demonstrates the magnetic field-induced transition from wave turbulence to shock waves on a fluid surface and models the spectral and statistical properties of shocks.

Findings

Transition from gravity-capillary wave turbulence to shock waves with increased magnetic field

Shock waves produce an $ extomega^{-4}$ power spectrum consistent with a Kuznetsov-like model

Shock amplitude statistics follow a power-law distribution close to Burgers equation predictions

Abstract

We report on the experimental observation of a transition from a dispersive wave turbulence regime to a nondispersive regime involving shock waves on the surface of a fluid. We use a magnetic fluid in a canal subjected to an external horizontal magnetic field to tune the dispersivity of the system. For a low magnetic field, gravity-capillary wave turbulence is observed, whereas for a high enough field, random steep coherent structures arise which are found to be shock waves. These shock waves create singularities in the second-order difference of the surface elevation, leading to an $\omega^{-4}$ frequency power spectrum. This spectrum is also found to be controlled by the number and amplitude of the shocks and is well captured by a model based on a random Dirac-$\delta$ distribution (Kuznetsov-like spectrum). Finally, the shock-amplitude statistics exhibits a power-law distribution with an exponent close to the predictions of the one-dimensional random-forced Burgers equation. This shock-wave regime, discovered here for surface waves, thus paves the way to better explore their properties.