Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

Kochurin, E. A.; Ricard, Guillaume; Зубарев, Н. М.; Falcon, Éric

doi:10.1103/physreve.105.l063101

Cited by 10 publications

(3 citation statements)

References 41 publications

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“…Although subjected to dissipation during their propagation, shock waves are thus coherent structures rich in the frequency domain. Note that the Maxwell stress which should decrease the wave height in the magnetic field direction [23,25] is not reported here. This higher-order effect could occur at higher v A not experimentally achievable in our parameter range (see Appendix C).…”

Section: B Surface Elevation Signals and Time-frequency Analysismentioning

confidence: 99%

“…The latter modifies the dispersion relationship of surface waves adding a nondispersive term that is tunable experimentally [23]. In this case, dispersive wave turbulence is evidenced experimentally in two dimensions because of the anisotropic dispersion relation, nondispersivity occurring only in the magnetic field direction [24,25]. Another method to experimentally control the wave dispersion is to decrease the fluid depth of gravity-capillary wave turbulence from a deep regime to a shallow one [26,27].…”

Section: Introductionmentioning

confidence: 99%

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Transition from wave turbulence to acousticlike shock-wave regime

Ricard¹,

Falcon²

2023

Preprint

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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 ω −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-δ 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.

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Section: B Surface Elevation Signals and Time-frequency Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transition from wave turbulence to acousticlike shock-wave regime

Ricard¹,

Falcon²

2023

Preprint

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“…The Zubarev solution for surface electro-hydrodynamic waves is a complete analog of Alf ven waves in plasmas, which play an important role in the development of magneto-hydrodynamic (MHD) turbulence [11]. Free-surface magnetic (or electric) wave turbulence as an analog to classic MHD turbulence was studied experimentally and theoretically in [12][13][14] and [15][16][17], respectively.…”

Section: Introductionmentioning

confidence: 99%

Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields

Flamarion,

Kochurin,

Ribeiro-Jr

2023

Mathematics

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This work presents the results of a direct numerical simulation of the nonlinear free surface evolution of a finite-depth fluid with a linear shear flow under the action of horizontal electric fields. The method of time-dependent conformal transformation for the description of the combined effects of the electric fields and constant vorticity is generalized for the first time. The simulation results show that strong shear flow co-directed in the wave propagation direction leads to the formation of large-amplitude surface waves, and, for some limiting vorticity value, a wave breaking process with the formation of an air bubble in the liquid is possible. The oppositely directed shear flow can cause the retrograde motion of a surface wave (wave propagation in the opposite direction to the linear wave speed). The simulations conducted taking into account the electro-hydrodynamic effects demonstrate that a high enough external horizontal electric field suppresses these strongly nonlinear processes, and the surface waves tend to preserve their shape.

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Wave turbulence and the kinetic equation beyond leading order

Rosenhaus,

Smolkin

2024

Phys. Rev. E

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Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

Cited by 10 publications

References 41 publications

Transition from wave turbulence to acousticlike shock-wave regime

Transition from wave turbulence to acousticlike shock-wave regime

Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields

Wave turbulence and the kinetic equation beyond leading order

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