The effects of a simple shear layer on the growth of Kelvin–Helmholtz instabilities

In this paper we study Kelvin–Helmholtz instabilities for the case of a linear shear in an inviscid compressible homogeneous fluid. We find that such a shear destabilizes zero growth vortex sheet modes when the Mach number (defined in terms of half the relative velocity across the shear) is sufficiently high. A comparison is drawn between our work for a linear shear, and earlier work on a hyperbolic tangent shear. Close parallels are seen in the results of these two velocity profiles.