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Nonlinear stability of surface waves in magnetic fluids: effect of a periodic 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 University, Heliopolis, Cairo, Egypt
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Abstract

Nonlinear wave propagation on the surface between two superposed magnetic fluids stressed by a tangential periodic magnetic field is investigated using the method of multiple scales. A stability analysis reveals the existence of both nonresonant and resonant cases. From the solvability conditions, three types of nonlinear Schrodinger equation are obtained. The necessary and sufficient conditions for stability are obtained in each case. Formulae for the surface elevation are also obtained in both the non-resonant and the resonant cases. It is found from the numerical calculation that the tangential periodic magnetic field plays a dual role in the stability criterion, while the field frequency has a destabilizing influence.

Type
Research Article
Information
Journal of Plasma Physics , Volume 49 , Issue 2 , April 1993 , pp. 317 - 330
Copyright
Copyright © Cambridge University Press 1993

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