Title

An Analytical Study Of The Kelvin-Helmholtz Instabilities Of Compressible, Magnetized Tangential Velocity Discontinuities With Generalized Polytrope Laws

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 stabile 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) ≤ 1.

Publication Date

1-1-2002

Publication Title

Quarterly of Applied Mathematics

Volume

60

Issue

4

Number of Pages

601-630

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/qam/1938343

Socpus ID

0036905883 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0036905883

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