Journal Article

Mean-field effects in the Galloway–Proctor flow

Karl-Heinz Rädler and Axel Brandenburg

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 393, issue 1, pages 113-125
Published in print February 2009 | ISSN: 0035-8711
Published online January 2009 | e-ISSN: 1365-2966 | DOI:
Mean-field effects in the Galloway–Proctor flow

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In the framework of mean-field electrodynamics the coefficients defining the mean electromotive force in Galloway–Proctor flows are determined. These flows show a two-dimensional pattern and are helical. The pattern wobbles in its plane. Apart from one exception a circularly polarized Galloway–Proctor flow, i.e. a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes & Tobias. An analytic theory of the α effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an α effect but no γ effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for α and show that γ is in general non-zero. Both α and γ show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the circular motion. Some results for the magnetic diffusivity ηt and a related quantity are given, too. Finally, a result for α in the case of a randomly varying linearly polarized Galloway–Proctor flow, without the aforementioned circular motion, is presented. The flows investigated show quite interesting effects. There is, however, no straightforward way to relate these flows to turbulence and to use them for studying properties of the α effect and associated effects under realistic conditions.

Keywords: hydrodynamics; magnetic fields; MHD; turbulence

Journal Article.  8127 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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