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The decay of wall-bounded MHD turbulence at low $Rm$

Published online by Cambridge University Press:  26 October 2015

Alban Pothérat  and
Kacper Kornet
Alban Pothérat*
Affiliation:
Applied Mathematics Research Centre, Coventry University, Coventry CV51FB, UK
Kacper Kornet
Affiliation:
Applied Mathematics Research Centre, Coventry University, Coventry CV51FB, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present direct numerical simulations of decaying magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number. The domain considered is bounded by periodic boundary conditions in the two directions perpendicular to the magnetic field and by two plane Hartmann walls in the third direction. Regimes of high magnetic fields (Hartmann number of up to 896) are reached thanks to a new spectral method using the eigenvectors of the dissipation operator. The decay is found to proceed through two phases: first, energy and integral length scales vary rapidly during a two-dimensionalisation phase extending over approximately a Hartmann friction time. During this phase, the evolution of the former appears significantly more impeded by the presence of walls than that of the latter. Once the large scales are nearly quasi-two-dimensional, the decay results from the competition of a two-dimensional dynamics driven by dissipation in the Hartmann boundary layers and the three-dimensional dynamics of smaller scales. In the later stages of the decay, three-dimensionality subsists under the form of barrel-shaped structures. A purely quasi-two dimensional decay entirely dominated by friction in the Hartmann layers is not reached because of residual dissipation in the bulk. However, this dissipation is not generated by the three-dimensionality that subsists, but by residual viscous friction due to horizontal velocity gradients. In the process, the energy in the velocity component aligned with the magnetic field is found to be strongly suppressed, as is skewness. This result reproduces the experimental findings of Kolesnikov & Tsinober (Fluid Dyn., vol. 9, 1974, pp. 621–624), where, as in the present simulations, Hartmann walls were present.

JFM classification

MHD and Electrohydrodynamics: High-Hartmann-number flows MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 605 - 636
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Copyright
© 2015 Cambridge University Press 

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