The combined influence of rarefaction and compressibility on classical Kelvin-Helmholtz instability is investigated with numerical simulations employing the unified gas kinetic scheme. Five different regimes in the Reynolds-Mach-Knudsen number parameter space are identified. The flow features in various Mach and Knudsen number regimes are examined. Stabilizing action of compressibility leads to suppression of perturbation kinetic energy and vorticity and/or momentum thickness. The suppression due to rarefaction exhibits a different behavior. At high enough Knudsen numbers, even as the perturbation kinetic energy is suppressed, the vorticity and/or momentum thickness grows. The flow physics underlying the contrasting mechanisms of compressibility and rarefaction is highlighted.
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