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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(2):211-248; doi:10.1093/qjmam/46.2.211
© 1993 by Oxford University Press
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THE EFFECT OF A UNIFORM MAGNETIC FIELD ON THE ONSET OF MARANGONI CONVECTION IN A LAYER OF CONDUCTING FLUID

S. K. WILSON{dagger}

( School of Mathematics, University of East Anglia Norwich NR4 7TJ )

{dagger}Present address: Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH.

In this paper we use a combination of analytical and numerical techniques to analyse the effect of a uniform vertical magnetic field on the onset of Marangoni convection in a horizontal layer of quiescent electrically conducting fluid subject to a uniform vertical temperature gradient. Both steady and overstable modes are considered and in the course of the analysis we correct a number of inaccuracies in the work of earlier authors. We conclude that the presence of the magnetic field always has a stabilizing effect on the flow, but that certain wave numbers will always remain unstable to steady convection however strong the magnetic field is.


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