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Double-diffusive convection with two stabilizing gradients: strange consequences of magnetic buoyancy

Published online by Cambridge University Press:  26 April 2006

D. W. Hughes  and
N. O. Weiss
D. W. Hughes
Affiliation:
Department of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK Present address: Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK.
N. O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

Instabilities due to a vertically stratified horizontal magnetic field (magnetic buoyancy instabilities) are believed to play a key role in the escape of the Sun's internal magnetic field and the formation of active regions and sunspots. In a star the magnetic diffusivity is much smaller than the thermal diffusivity and magnetic buoyancy instabilities are double-diffusive in character. We have studied the nonlinear development of these instabilities, in an idealized two-dimensional model, by exploiting a non-trivial transformation between the governing equations of magnetic buoyancy and those of classical thermosolutal convection. Our main result is extremely surprising. We have demonstrated the existence of finite-amplitude steady convection when both the influential gradients (magnetic and convective) are stabilizing. This strange behaviour is caused by the appearance of narrow magnetic boundary layers, which distort the mean pressure gradient so as to produce a convectively unstable stratification.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 301 , 25 October 1995 , pp. 383 - 406
Copyright
© 1995 Cambridge University Press

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