The magnetohydrodynamic Kelvin-Helmholtz instability. III. The role of sheared magnetic field in planar flows

We have carried out simulations of the nonlinear evolution of the magnetohy drodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible fluids in 2.5 dimensions, extending our previous work by Frank et al. and Jones et al. In the present work we have simulated flows in the x-y plane in which a "sheared" magnetic held of uniform strength smoothly rotates across a thi n velocity shear layer from the z-direction to the x-direction, aligned wit h the flow field. The sonic Mach number of the velocity transition is unity . Such hows containing a uniform held in the x-direction are linearly stabl e if the magnetic held strength is great enough that the Alfvenic Mach numb er M-A = U-0/c(A) < 2. That limit does not apply directly to sheared magnet ic fields, however, since the z-field component has almost no influence on the linear stability. Thus, if the magnetic shear layer is contained within the velocity shear layer, the KH instability may still grow, even when the field strength is quite large. So, here we consider a wide range of sheare d field strengths covering Alfvenic Mach numbers, M-A = 142.9 to 2. We focus on dynamical evolution of fluid features, kinetic energy dissipati on, and mixing of the fluid between the two layers, considering their depen dence on magnetic held strength for this geometry. There are a number of di fferences from our earlier simulations with uniform magnetic fields in the x-y plane. For the latter, simpler case we found a clear sequence of behavi ors with increasing field strength ranging from nearly hydrodynamic flows i n which the instability evolves to an almost steady cat's eye vortex with e nhanced dissipation, to hows in which the magnetic field disrupts the cat's eye once it forms, to, finally, flows that evolve very little before held- line stretching stabilizes the velocity shear layer. The introduction of ma gnetic shear can allow a cat's eye-like vortex to form, even when the held is stronger than the nominal linear instability limit given above. For stro ng fields that vortex is asymmetric with respect to the preliminary shear l ayer, however, so the subsequent dissipation is enhanced over the uniform h eld cases of comparable held strength. In fact, so long as the magnetic fie ld achieves some level of dynamical importance during an eddy turnover time , the asymmetries introduced through the magnetic shear will increase flow complexity and, with that, dissipation and mixing. The degree of the fluid mixing between the two layers is strongly influenced by the magnetic field strength. Mixing of the fluid is most effective when the vortex is disrupte d by magnetic tension during transient reconnection, through local chaotic behavior that follows.