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Two-dimensional magnetohydrodynamic turbulence in the small magnetic Prandtl number limit

Published online by Cambridge University Press:  14 June 2012

David G. Dritschel  and
Steven M. Tobias
David G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
Steven M. Tobias*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: smt@amsta.leeds.ac.uk
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Abstract

In this paper we introduce a new method for computations of two-dimensional magnetohydrodynamic (MHD) turbulence at low magnetic Prandtl number . When , the magnetic field dissipates at a scale much larger than the velocity field. The method we utilize is a novel hybrid contour–spectral method, the ‘combined Lagrangian advection method’, formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudo-spectral method for decreasing for the problem of decaying two-dimensional MHD turbulence. The method is shown to agree well for a wide range of imposed magnetic field strengths. Examples of problems for which such a method may prove invaluable are also given.

JFM classification

Mathematical Foundations: Computational methods MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 85 - 98
Copyright
Copyright © Cambridge University Press 2012

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