We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability in a compressible fluid layer with and without a weak magnetic field. In the absence of a magnetic field, the instability generates a single eddy that flattens the velocity profile, stabilizing it against further perturbations. Adding a weak magnetic field—weak in the sense that it has almost no effect on the linear instability—leads to a complex flow morphology driven by MHD forces and to enhanced broadening of the layer due to Maxwell stresses. We corroborate earlier studies, which showed that magnetic fields destroy the large-scale eddy structure through periodic cycles of windup and resistive decay, but we show that the rate of decay decreases with decreasing plasma resistivity η, at least within the range of η accessible to our simulations. Magnetization increases the efficiency of momentum transport, and the transport increases with decreasing η.
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