A spatiotemporal linear stability analysis is performed on a confined two-dimensional shear flow to investigate the effects of compressibility on its absolute stability characteristics. The unsteady perturbation is decomposed into varicose and sinuous modes. As the shear Mach number increases from low subsonic to low supersonic values, the varicose mode under very strong or very weak confinement stabilizes, while that under moderate confinement destabilizes. Within the subsonic and low supersonic regime, the sinuous mode of strongly confined and weakly confined jets destabilizes with the increase of the shear Mach number, while that of moderately confined jets stabilizes. The sinuous mode of a subsonic wake, however, is stabilized as the shear Mach number increases. At low supersonic shear Mach numbers, insensitivity of both the varicose and sinuous modes to confinement is observed for certain ranges of parameters. At high supersonic shear Mach numbers, a new absolutely unstable varicose mode that remains stable at low shear Mach numbers is identified. In particular, this mode is shown to dominate the long-time impulse response under certain conditions. A clear characterization of these stability behaviors is important in applications such as high-speed jets in rocket and aeroacoustic facilities.

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• Flow instability