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Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

Ilin, K.I. and Vladimirov, V.A. (2004) Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation. Physics of Plasmas, 11 (7). pp. 3586-3594. ISSN 1089-7674

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Abstract

The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Physics (York)
Depositing User: York RAE Import
Date Deposited: 24 Feb 2009 10:44
Last Modified: 24 Feb 2009 10:44
Published Version: http://dx.doi.org/10.1063/1.1759337
Status: Published
Publisher: American Institute of Physics
Identification Number: 10.1063/1.1759337
URI: http://eprints.whiterose.ac.uk/id/eprint/7246

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