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A bicharacteristic formulation of the ideal MHD equations

Published online by Cambridge University Press:  13 April 2010

HARI SHANKER GUPTA  and
PHOOLAN PRASAD
HARI SHANKER GUPTA
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India ([email protected])
PHOOLAN PRASAD
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India ([email protected])
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Abstract

On a characteristic surface Ω of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Ω. This result can be interpreted also as a transport equation along rays of the wavefront Ωt in x-space associated with Ω. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

Type
Papers
Information
Journal of Plasma Physics , Volume 77 , Issue 2 , April 2011 , pp. 169 - 191
Copyright
Copyright © Cambridge University Press 2010

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