An analytical study of the Kelvin–Helmholtz instabilities of compressible, magnetized, anisotropic, and isotropic tangential velocity discontinuities

An analytical study is made of the linear stability of tangential velocity discontinuities in anisotropic and isotropic compressible, magnetized plasmas. A new analytical technique leads to entirely new results for both cases, and recovers previously obtained numerical results for the isotropic case. For both the anisotropic and isotropic vortex sheets, the structure of unstable, standing wave modes is mapped out in the (inverse plasma beta, Mach number) plane for modes at arbitrary angles to the flow and the magnetic field. Solutions are obtained for unstable standing and traveling modes of the anisotropic vortex sheet propagating parallel or antiparallel to the magnetic field, and at small angles to these directions. Numerically computed unstable standing modes obtained previously for the isotropic case are recovered analytically and extended to more general configurations. Also, it is shown that modes propagating along or opposite to the magnetic field direction, and at a general angle to the flow, do not exhibit standing wave instability for (plasma beta)≤1, for the isotropic vortex sheet.