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Turbulence in electromagnetically driven Keplerian flows

Published online by Cambridge University Press:  12 August 2021

M. Vernet Open the ORCID record for M. Vernet [Opens in a new window] ,
M. Pereira Open the ORCID record for M. Pereira [Opens in a new window] ,
S. Fauve Open the ORCID record for S. Fauve [Opens in a new window]  and
C. Gissinger Open the ORCID record for C. Gissinger [Opens in a new window]
M. Vernet*
Affiliation:
Laboratoire de Physique de l'Ecole Normale Superieure, CNRS, PSL Research University, Sorbonne Universite, Universite de Paris, F-75005 Paris, France
M. Pereira
Affiliation:
Arts et Metiers Institute of Technology, CNAM, LIFSE, HESAM University, F-75013 Paris, France
S. Fauve
Affiliation:
Laboratoire de Physique de l'Ecole Normale Superieure, CNRS, PSL Research University, Sorbonne Universite, Universite de Paris, F-75005 Paris, France
C. Gissinger
Affiliation:
Laboratoire de Physique de l'Ecole Normale Superieure, CNRS, PSL Research University, Sorbonne Universite, Universite de Paris, F-75005 Paris, France Institut Universitaire de France (IUF), Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian velocity profiles. For very large current I and moderate magnetic field B, we observe a new regime, fully turbulent, which exhibits large fluctuations and a Keplerian mean rotation profile $\varOmega \sim {\sqrt {IB}}/{r^{3/2}}$, where r is the distance from the axis. In this turbulent regime, the dynamics is typical of thin layer turbulence, characterized by a direct cascade of energy towards the small scales and an inverse cascade to large scales. Finally, at very large magnetic field, this turbulent flow bifurcates to a quasi-bidimensional turbulent flow involving the formation of a large scale condensate in the horizontal plane. These results are well understood as resulting from an instability of the Bödewadt–Hartmann layers at large Reynolds number and discussed in the framework of similar astrophysical flows.

JFM classification

Instability: Transition to turbulence MHD and Electrohydrodynamics: MHD turbulence Boundary Layers: Boundary layer stability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A29
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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