Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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An analytical study of the Kelvin-Helmholtz instabilities of compressible, magnetized tangential velocity discontinuities with generalized polytrope laws


Authors: Kevin G. Brown and S. Roy Choudhury
Journal: Quart. Appl. Math. 60 (2002), 601-630
MSC: Primary 76E25; Secondary 76E20, 76X05
DOI: https://doi.org/10.1090/qam/1938343
MathSciNet review: MR1938343
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Abstract: The linear Kelvin-Helmholtz instability of tangential velocity discontinuities in high velocity magnetized plasmas with isotropic or anisotropic pressure is investigated. A new analytical technique applied to the magnetohydrodynamic equations with generalized polytrope laws (for the pressure parallel and perpendicular to the magnetic field) yields the complete structure of the unstable, standing waves in the (inverse plasma beta, Mach number) plane for modes at arbitrary angles to the flow and the magnetic field. The stable regions in the (inverse plasma beta, propagation angle) plane are mapped out via a level curve analysis, thus clarifying the stabilizing effects of both the magnetic field and the compressibility. For polytrope indices corresponding to the double adiabatic and magnetohydrodynamic equations, the results reduce to those obtained earlier using these models. Detailed numerical results are presented for other cases not considered earlier, including the cases of isothermal and mixed waves. Also, for modes propagating along or opposite to the magnetic field direction and at general angles to the flow, a criterion is derived for the absence of standing wave instability--in the isotropic MHD case, this condition corresponds to (plasma beta) $ \le 1$.


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DOI: https://doi.org/10.1090/qam/1938343
Article copyright: © Copyright 2002 American Mathematical Society


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