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Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field

Published online by Cambridge University Press:  13 March 2009

Yusry O. El-Dib
Yusry O. El-Dib
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams Unviersity, Heliopolis, Cairo, Egypt
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Abstract

The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 1 , February 1994 , pp. 1 - 11
Copyright
Copyright © Cambridge University Press 1994

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