Kelvin-Helmholtz instabilities of supersonic, magnetized shear layers

The linear stability of finite-thickness, compressible, ideal magnetohydrodynamic sheared flows along the z direction, with a magnetic field in the (y, z) plane is studied. This paper extends earlier work with the magnetic field parallel to the flow. The present formulation also includes the effects of density and pressure gradients in the equilibrium shear layer. Analytical solutions are obtained for strongly and weakly magnetized shear layers having a vortex sheet profile (where the velocity is a step function). For an equilibrium layer having a linear velocity profile, and uniform pressure and density, contour plots of the real and imaginary parts of the perturbation frequency (corresponding to unstable waves) are numerically generated in (wavenumber, Mach number) plane using a shooting technique. The structure of two distinct regimes of instability (unstable standing modes and unstable travelling modes) is mapped out for various values of the inverse plasma beta, and various angles of propagation of the mode to the flow and the magnetic field.