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Nonlinear magnetohydrodynamic stability for axisymmetric incompressible ideal flows

Published online by Cambridge University Press:  31 January 2002

A. H. KHATER ,
M. A. HELAL ,
D. K. CALLEBAUT  and
S. M. MOAWAD
A. H. KHATER
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Beni-Suef, Egypt Present address: Mathematics Department, Faculty of Science, King Khalid University, Abha, Kingdom of Saudi Arabia
M. A. HELAL
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
D. K. CALLEBAUT
Affiliation:
Department Natuurkunde, Universiteit Antwerpen (UIA), Universiteitsplein 1, B-2610 Antwerp, Belgium
S. M. MOAWAD
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Beni-Suef, Egypt
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Abstract

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In this paper, the general theory developed by Vladimirov and Moffatt [J. Fluid Mech.283, 125–139 (1995)] and Vladimirov et al. [J. Fluid Mech.329, 187–205 (1996); J. Plasma Phys.57, 89–120 (1997)] is extended to nonlinear (Lyapunov) stability for axisymmetric (invariant under rotations around fixed axis) solutions of the ideal incompressible magnetohydrodynamic flows for a situation of arbitrary flow and a poloidal field. The appropriate norm is the sum of magnetic and kinetic energies and the mean square vector potential of the magnetic field.

Type
Research Article
Information
Journal of Plasma Physics , Volume 66 , Issue 1-2 , July 2001 , pp. 1 - 25
Copyright
2001 Cambridge University Press