Journal Article

Closure tests for mean field magnetohydrodynamics using a self-consistent reduced model

V. V. Pipin and M. R. E. Proctor

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 388, issue 1, pages 367-374
Published in print July 2008 | ISSN: 0035-8711
Published online July 2008 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.13396.x
Closure tests for mean field magnetohydrodynamics using a self-consistent reduced model

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The mean electromotive force and α effect are computed for a forced turbulent flow using a simple non-linear dynamical model. The results are used to check the applicability of two basic analytic ansätze of mean-field magnetohydrodynamics – the second-order correlation approximation (SOCA) and the τ approximation. In the numerical simulations the effective Reynolds number Re is 2–20, while the magnetic Prandtl number Pm varies from 0.1 to 107. We present evidence that the τ approximation may be appropriate in dynamical regimes where there is a small-scale dynamo. Catastrophic quenching of the α effect is found for high Pm. Our results indicate that for high Pm SOCA gives a very large value of the α coefficient compared with the ‘exact’ solution. The discrepancy depends on the properties of the random force that drives the flow, with a larger difference occurring for δ-correlated force compared with that for a steady random force.

Keywords: turbulence; Sun: activity; Sun: magnetic fields

Journal Article.  3901 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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