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

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Dritschel2012JFluidMech703_MagnetohydrodynamicTurbulence.pdf (7.675Mb)
Date
01/07/2012
Author
Dritschel, David Gerard
Tobias, Steve
Keywords
Computational methods
MHD turbulence
Turbulence simulation
QA Mathematics
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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 $\Pra=\nu/\eta$. When $\Pra \ll 1$, the magnetic field dissipates at a scale much larger than the velocity field. The method we utilise 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 $\Pra$ 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.
Citation
Dritschel , D G & Tobias , S 2012 , ' Two-dimensional magnetohydrodynamic turbulence in the small magnetic Prandtl number limit ' , Journal of Fluid Mechanics , vol. 703 , pp. 85-98 . https://doi.org/10.1017/jfm.2012.195
Publication
Journal of Fluid Mechanics
Status
Peer reviewed
DOI
https://doi.org/10.1017/jfm.2012.195
ISSN
0022-1120
Type
Journal article
Rights
Copyright (c) Cambridge University Press 2012
Collections
  • Applied Mathematics Research
  • Scottish Oceans Institute Research
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/3698

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