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Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

Published online by Cambridge University Press:  14 June 2013

S. M. MOAWAD
S. M. MOAWAD*
Affiliation:
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt (smmoawad@hotmail.com)
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Abstract

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Issue 5 , October 2013 , pp. 873 - 883
Copyright
Copyright © Cambridge University Press 2013 

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