The magnetohydrodynamic Kelvin-helmholtz instability: A three-dimensional study of nonlinear evolution

We investigate through high-resolution three-dimensional simulations the no nlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. As in our earlier work, we have considered pe riodic sections of flows that contain a thin, transonic shear layer but are otherwise uniform. The initially uniform magnetic field is parallel to the shear plane but oblique to the flow itself. We confirm in three-dimensiona l flows the conclusion from our two-dimensional work that even apparently w eak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fa ct, that statement is strengthened in three dimensions by this work because it shows how field-line bundles can be stretched and twisted in three dime nsions as the quasi-two-dimensional Cat's Eye vortex forms out of the hydro dynamical motions. In our simulations twisting of the field may increase th e maximum field strength by more than a factor of 2 over the two-dimensiona l effect. If, by these developments, the Mach number of Alfven flows around the Cat's Eye drops to unity or less, our simulations suggest that magneti c stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that r etains memory of the original shear. For our flow configurations, the regim e in three dimensions for such reorganization is 4 less than or similar to M-Ax less than or similar to 50, expressed in terms of the Alfven Mach numb er of the original velocity transition and the initial speed projected to t he flow plan. When Alfven the initial field is stronger than this, the flow either is linearly stable (if M-Ax less than or similar to 2) or becomes s tabilized by enhanced magnetic tension as a result of the corrugated field along the shear layer before the Cat's Eye forms (if M-Ax greater than or s imilar to2). For weaker fields the instability remains essentially hydrodyn amic in early stages, and the Cat's Eye is destroyed by the hydrodynamic se condary instabilities of a three-dimensional nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In th is stage, there is considerable enhancement to the magnetic energy due to s tretching, twisting, and turbulent amplification, which is retained long af terward. The magnetic energy eventually catches up to the kinetic energy, a nd the nature of flows becomes magnetohydrodynamic. Decay of the magnetohyd rodynamic turbulence is enhanced by dissipation accompanying magnetic recon nection. Hence, in three dimensions as in two dimensions, very weak fields do not modify substantially the character of the flow evolution but do incr ease global dissipation rates.