Transition from wave turbulence to acousticlike shock-wave regime

Guillaume Ricard and Eric Falcon

Université Paris Cité, MSC Laboratory, UMR 7057 CNRS, F-75 013 Paris, France



Reference: Physical Review Fluids 8, 014804 (2023)   

URL: https://link.aps.org/doi/10.1103/PhysRevFluids.8.014804
DOI: 10.1103/PhysRevFluids.8.014804
 

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 a ω4\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 1D random-forced Burgers equation. To our knowledge this shock-wave regime has not previously been examined for surface waves and paves the way to better explore their properties.

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