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Instabilities of dynamic thermocapillary liquid layers with magnetic fields

Published online by Cambridge University Press:  10 March 1999

T. E. MORTHLAND  and
J. S. WALKER
T. E. MORTHLAND
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, USA Present address: 1206 W. Green St., Urbana, IL 61801, USA.
J. S. WALKER
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, USA
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Abstract

This paper presents a linear-stability analysis for the transition from a steady, two-dimensional thermocapillary convection in a liquid-metal layer to a periodic, three-dimensional flow involving hydrothermal waves which propagate in the directionzw normal to the plane of the base flow. There is a uniform magnetic field applied parallel to the free surface in the plane of the base flow, and there is a linear temperature gradient along the free surface in the base flow. The ratio of the layer's length to its depth, 2L, is large. The magnetic Reynolds number is small.

A key parameter is λ, the ratio of the large Hartmann number based on depth to L. The value of λ increases as either the magnetic field strength is increased or L is decreased. The results for very small values of λ agree with the results of a previous treatment of this instability without a magnetic field. As λ is increased, the critical Marangoni number and the wavenumber for the hydrothermal rolls both increase. For large values of λ, the base flow and the hydrothermal waves are confined to a free-surface layer with O(λ−2) dimensionless thickness.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 382 , 10 March 1999 , pp. 87 - 108
Copyright
© 1999 Cambridge University Press

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