Nonlocal stability analysis of the MHD KelvinHelmholtz instability in a compressible plasma
Abstract
A general stability analysis is performed for the KelvinHelmholtz instability is sheared magnetohydrodynamic flow of finite thickness in a compressible plasma. The analysis allows for arbitrary orientation of the magnetic field B_{0}, velocity flow v_{0}, and wave vector k in the plane perpendicular to the velocity gradient, and no restrictions are imposed on the sound or Alfvén Mach numbers. The stability problem is reduced to the solution of a singleorder differential equation, which includes a gravitational term to represent coupling between the KelvinHelmholtz mode and the interchange mode. In the incompressible limit it is shown that the KelvinHelmholtz mode is completely stabilized for any velocity profile as long as the condition V_{0}<2v_{A} (k.B_{0})/(k.v_{0}) is satisfied, where V_{0} is the total velocity jump across the shear layer. Numerical results are obtained for a hyperbolic tangent velocity profile for the transverse (B_{0}⊥v_{0}) and parallel (B_{0}∥v_{0}) flow configurations. Only modes with k∆<2 are unstable, where ∆ is the scale length of the shear layer. The fastest growing modes occur for k∆~0.51.0. 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 k.B_{0}≠0, the instability contains Alfvénmode and slowmode components as well. The Alfvén component gives rise to a fieldaligned current inside the shear layer. In the parallel case, both Alfvén and slow magnetosonic components are present, with the Alfvén 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 KelvinHelmholtz mode has a frequency of 0 (V_{0}/2∆), which overlaps with the frequency range of geomagnetic pulsations (Pc 35). It is suggested that the MHD KelvinHelmholtz instability could serve as a dynamo process driving smallscale fieldaligned currents in the presence of the sheared plasma flow in the magnetosphere.
 Publication:

Journal of Geophysical Research
 Pub Date:
 September 1982
 DOI:
 10.1029/JA087iA09p07431
 Bibcode:
 1982JGR....87.7431M
 Keywords:

 KelvinHelmholtz Instability;
 Magnetohydrodynamic Stability;
 Solar Wind;
 Space Plasmas;
 Compressible Fluids;
 Eigenvalues;
 Magnetopause;
 Solar Terrestrial Interactions;
 Geophysics