A bicharacteristic formulation of the ideal MHD equations

Gupta, Hari Shanker ; Prasad, Phoolan (2011) A bicharacteristic formulation of the ideal MHD equations Journal of Plasma Physics, 77 (2). pp. 169-191. ISSN 0022-3778

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Related URL: http://dx.doi.org/10.1017/S0022377810000176


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.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
ID Code:37674
Deposited On:25 Apr 2011 10:20
Last Modified:17 May 2016 20:33

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