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Compressible Magnetoconvection in Three Dimensions

Published online by Cambridge University Press:  11 May 2010

P. C. Matthews
Affiliation:
Department of Applied Mathematics and Theoretical Physics University of Cambridge, Silver St., Cambridge, CB3 9EW UK
M. R. E. Proctor
Affiliation:
University of Cambridge
P. C. Matthews
Affiliation:
University of Cambridge
A. M. Rucklidge
Affiliation:
University of Cambridge
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Summary

Convection in a compressible fluid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry, restricting attention to the weakly nonlinear regime. Steady convection occurs in the form of two-dimensional rolls when the field is weak but three-dimensional squares when the magnetic field is sufficiently strong. In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be ‘alternating rolls’ – standing waves in both horizontal directions which are out of phase. For stronger fields, oscillatory convection takes the form of a two-dimensional travelling wave.

INTRODUCTION

This paper is concerned with the effect of an imposed magnetic field on thermal convection. Although this is not directly relevant to dynamo theory, the question of the interaction of convection with magnetic fields is important for a full understanding of a convectively driven dynamo. The motivation for this work is to understand some aspects of convection in the Sun, particularly in regions of high magnetic field, such as sunspots, where the strong, predominantly vertical field inhibits thermal convection, causing the spot to appear dark. This work is part of an ongoing collaboration with Michael Proctor and Nigel Weiss. This brief report summarises some of the main results of this work; further details will be published in a future paper (Matthews, Proctor & Weiss 1993).

Linear theory for the onset of magnetoconvection in an incompressible fluid was discussed extensively by Chandrasekhar (1961).

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Publisher: Cambridge University Press
Print publication year: 1994

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