The MHD Kelvin-Helmholtz Instability II: The Roles of Weak and Oblique Fields in Planar Flows

Abstract

We have carried out high resolution MHD simulations of the nonlinear evolution of Kelvin-Helmholtz unstable flows in 2 1/2 dimensions. The modeled flows and fields were initially uniform except for a thin shear layer with a hyperbolic tangent velocity profile and a small, normal mode perturbation. The calculations consider periodic sections of flows containing magnetic fields parallel to the shear layer, but projecting over a full range of angles with respect to the flow vectors. They are intended as preparation for fully 3D calculations and to address two specific questions raised in earlier work: 1) What role, if any, does the orientation of the field play in nonlinear evolution of the MHD Kelvin-Helmholtz instability in 2 1/2 D. 2) Given that the field is too weak to stabilize against a linear perturbation of the flow, how does the nonlinear evolution of the instability depend on strength of the field. The magnetic field component in the third direction contributes only through minor pressure contributions, so the flows are essentially 2D. Even a very weak field can significantly enhance the rate of energy dissipation. In all of the cases we studied magnetic field amplification by stretching in the vortex is limited by tearing mode, ``fast'' reconnection events that isolate and then destroy magnetic flux islands within the vortex and relax the fields outside the vortex. If the magnetic tension developed prior to reconnection is comparable to Reynolds stresses in the flow, that flow is reorganized during reconnection. Otherwise, the primary influence on the plasma is generation of entropy. The effective expulsion of flux from the vortex is very similar to that shown by Weiss for passive fields in idealized vortices with large magnetic Reynolds numbers. We demonstrated that this