On stability of Alfvén discontinuities |
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Authors: | Konstantin Ilin Yuri Trakhinin |
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Institution: | 1. Department of Mathematics, University of York, Heslington, York YO10, U.K.;2. Sobolev Institute of Mathematics, Koptyuga pr. 4, 630090 Novosibirsk, Russia |
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Abstract: | We study Alfvén discontinuities for the equations of ideal compressible magnetohydrodynamics (MHD). The Alfvén discontinuity is a characteristic discontinuity for the hyperbolic system of the MHD equations but, as for shock waves, the gas crosses its front. By numerical testing of the Lopatinskii condition, we carry out spectral stability analysis, i.e. we find the parameter domains of stability and violent instability of planar Alfvén discontinuities. We also show that Alfvén discontinuities can be only weakly stable in the sense that the uniform Lopatinskii condition is never satisfied. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | hyperbolic systems of conservation laws shock waves and characteristic discontinuities mathematical fluid dynamics fluid mechanics magnetohydrodynamics hydrodynamic stability |
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