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We have carried out simulations of the nonlinear evolution of the magnetohydrodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible fluids in $2\frac{1}{2}$-dimensions, extending our previous work by Frank et al (1996) and Jones \etal (1997). In the present work we have simulated flows in the x-y plane in which a ``sheared'' magnetic field of uniform strength ``smoothly'' rotates across a thin velocity shear layer from the z direction to the x direction, aligned with the flow field. We focus on dynamical evolution of fluid features, kinetic energy dissipation, and mixing of the fluid between the two layers, considering their dependence on magnetic field strength for this geometry. The introduction of magnetic shear can allow a Cat's Eye-like vortex to form, even when the field is stronger than the nominal linear instability limit given above. For strong fields that vortex is asymmetric with respect to the preliminary shear layer, however, so the subsequent dissipation is enhanced over the uniform field cases of comparable field strength. In fact, so long as the magnetic field 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 disrupted by magnetic tension during transient reconnection, through local chaotic behavior that follows

The Magnetohydrodynamic Kelvin‐Helmholtz Instability. III. The Role of Sheared Magnetic Field in Planar Flows