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Turbulent resistivity in wavy two-dimensional magnetohydrodynamic turbulence

Published online by Cambridge University Press:  08 January 2008

SHANE R. KEATING  and
P. H. DIAMOND
SHANE R. KEATING
Affiliation:
Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
P. H. DIAMOND
Affiliation:
Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
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Abstract

The theory of turbulent resistivity in ‘wavy’ magnetohydrodynamic turbulence in two dimensions is presented. The goal is to explore the theory of quenching of turbulent resistivity in a regime for which the mean field theory can be rigorously constructed at large magnetic Reynolds number Rm. This is achieved by extending the simple two-dimensional problem to include body forces, such as buoyancy or the Coriolis force, which convert large-scale eddies into weakly interacting dispersive waves. The turbulence-driven spatial flux of magnetic potential is calculated to fourth order in wave slope – the same order to which one usually works in wave kinetics. However, spatial transport, rather than spectral transfer, is the object here. Remarkably, adding an additional restoring force to the already tightly constrained system of high Rm magnetohydrodynamic turbulence in two dimensions can actually increase the turbulent resistivity, by admitting a spatial flux of magnetic potential which is not quenched at large Rm, although it is restricted by the conditions of applicability of weak turbulence theory. The absence of Rm-dependent quenching in this wave-interaction-driven flux is a consequence of the presence of irreversibility due to resonant nonlinear three-wave interactions, which are independent of collisional resistivity. The broader implications of this result for the theory of mean field electrodynamics are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 173 - 202
Copyright
Copyright © Cambridge University Press 2008

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