On stability of Alfvén discontinuities

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JournalMathematical Methods in the Applied Sciences
DatePublished - Feb 2009
Issue number3
Volume32
Number of pages23
Pages (from-to)307-329
Original languageEnglish

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.

    Research areas

  • Fluid Dynamics, hyperbolic systems of conservation laws;, shock waves and characteristic discontinuities;, mathematical fluid dynamics;, fluid mechanics;, magnetohydrodynamics;, hydrodynamic stability

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