Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Kelvin-Helmholtz instabilities of high-velocity magnetized shear layers with generalized polytrope laws

Authors: Kevin G. Brown and S. Roy Choudhury
Journal: Quart. Appl. Math. 58 (2000), 401-423
MSC: Primary 76E25; Secondary 35Q35, 76E20, 76N99, 76W05
DOI: https://doi.org/10.1090/qam/1770646
MathSciNet review: MR1770646
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Abstract: The linear stability of zero and finite width, arbitrarily compressible, and magnetized velocity shear layers with isotropic or anisotropic pressure is investigated. Such flows, modeled by the magnetohydrodynamic equations with generalized polytrope laws for the pressure parallel and perpendicular to the magnetic field, are relevant in various astrophysical, geophysical and space plasma configurations. The conditions for instability of shear layers of zero width are derived. For layers of finite width, shooting numerical schemes are employed to satisfy the Sommerfeld radiation conditions of outgoing, spatially damping modes in a frame comoving with the plasma flow. The resulting eigenvalues for the angular frequency and linear growth rate are mapped out for different regions of the wave number/Mach number space. For polytrope indices corresponding to the double adiabatic and magnetohydrodynamic equations, the results reduce to those obtained earlier using these models.

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DOI: https://doi.org/10.1090/qam/1770646
Article copyright: © Copyright 2000 American Mathematical Society

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