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Spatial variations of magnetic permeability as a source of dynamo action

Published online by Cambridge University Press:  19 June 2013

B. Gallet ,
F. Pétrélis  and
S. Fauve
B. Gallet*
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
F. Pétrélis
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
S. Fauve
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
*
†Email address for correspondence: basile.gallet@gmail.com
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Abstract

We investigate dynamo action for a parallel flow of an electrically conducting fluid located over a boundary with spatially varying magnetic permeability. We first compute the dynamo threshold numerically. Then we perform an asymptotic expansion in the limit of small permeability modulation, which gives accurate results even for moderate modulation. We present in detail the mechanism at work for this dynamo. It is an interplay between shear (an $\omega $-effect) and a new conversion mechanism that originates from the non-uniform magnetic boundary. We illustrate how a similar mechanism leads to dynamo action in the case of spatially modulated electrical conductivity, a problem studied by Busse & Wicht (Geophys. Astrophys. Fluid Dyn., vol. 64, 1992, pp. 135–144). Finally, we discuss the relevance of this effect to experimental dynamos and present ways to increase the dynamo efficiency and reduce the instability threshold.

JFM classification

Nonlinear Dynamical Systems: Bifurcation MHD and Electrohydrodynamics: Dynamo theory MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 161 - 190
Copyright
©2013 Cambridge University Press 

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