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Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence

Published online by Cambridge University Press:  17 July 2009

CHRISTOPHER J. WAREING  and
RAINER HOLLERBACH
CHRISTOPHER J. WAREING
Affiliation:
Department of Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK (cjw@maths.leeds.ac.uk)
RAINER HOLLERBACH
Affiliation:
Department of Applied Mathematics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK (cjw@maths.leeds.ac.uk)
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Abstract

Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k−2 law with increasing RB, the ratio of the nonlinear to linear time scales in the governing equation, consistent with theoretical predictions. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer and recent studies of 2D EMHD turbulence. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. In another similarity to 2D EMHD turbulence, relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, cascades of energy in 3D EMHD turbulence are found to be suppressed in all directions under the influence of a uniform background field. Energy transfer is further reduced in the direction parallel to the field, displaying scale-dependent anisotropy. Finally, the governing equation is found to yield a weak inverse cascade, at least partially transferring magnetic energy from small to large scales.

Type
Papers
Information
Journal of Plasma Physics , Volume 76 , Issue 1 , February 2010 , pp. 117 - 128
Copyright
Copyright © Cambridge University Press 2009

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