Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma

Journal Article · Wed Sep 01 04:00:00 EDT 1982 · J. Geophys. Res.; (United States)

DOI:https://doi.org/10.1029/JA087iA09p07431· OSTI ID:6553659

Miura, A; Pritchett, P L

A general stability analysis is performed for the Kelvin-Helmholtz instability in sheared magnetohydrodynamic flow of finite thickness in a compressible plasma. The analysis allows for arbitrary orientation of the magnetic field B/sub 0/, velocity flow v/sub 0/, and wave vector k in the plane perpendicular to the velocity gradient, and no restrictions are imposed on the sound or Alfven Mach numbers. The stability problem is reduced to the solution of a single-order differential equation, which includes a gravitational term to represent coupling between the Kelvin-Helmholtz mode and the interchange mode. In the incompressible limit it is shown that the Kelvin-Helmholtz mode is completely stabilized for any velocity profile as long as the condition V/sub 0/<2v/sub A/ (kxB/sub 0/)/(kxv/sub 0/) is satisfied, where V/sub 0/ is the total velocity jump across the shear layer. Numerical results are obtained for a hyperbolic tangent velocity profile for the transverse (B/sub 0/perpendicularv/sub 0/) and parallel (B/sub 0/parallelv/sub 0/) flow configurations. Only modes with k..delta..<2 are unstable, where ..delta.. is the scale length of the shear layer. The fastest growing modes occur for k..delta..approx.0.5--1.0. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects. For the transverse case, only the fast magnetosonic mode is destabilized, but if the kxB/sub 0/not =0, the instability contains Alfven-mode and slow-mode components as well. The Alfven component gives rise to a field-aligned current inside the shear layer. In the parallel case, both Alfven and slow magnetosonic components are present, with the Alfven mode confined inside the shear layer. The results of the analysis are used to discuss the stability of sheared plasma flow at the magnetopause boundary and in the solar wind. At the magnetopause boundary, the fastest growing Kelvin-Helmholtz mode has a frequency of 0 (V/sub 0//2..delta..), which overlaps with the frequency range of geomagnetic pulsations (Pc 3--5).

• Research Organization: Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024
• OSTI ID: 6553659
• Journal Information: J. Geophys. Res.; (United States), Journal Name: J. Geophys. Res.; (United States) Vol. 87:A9; ISSN JGREA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPRESSIBLE FLOW
FLUID FLOW
FLUID MECHANICS
HELMHOLTZ INSTABILITY
HYDRODYNAMICS
INSTABILITY
MAGNETOHYDRODYNAMICS
MATHEMATICAL MODELS
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PLASMA INSTABILITY
PLASMA MACROINSTABILITIES