Stability of Non-Homentropic, Inviscid, Compressible Shear Flows

For non-homentropic, inviscid, compressible shear flows, the equivalent of Squire's theorem is proved. It is shown that a shear free basic flow does not support subsonic modes. Further, it is shown that the instability region for subsonic disturbances is a semi-ellipse type region, which depends on the Mach number, wave number, and depth of the fluid layer. Under an approximation, two estimates for the growth rate of an unstable subsonic mode are obtained. For unbounded flows, a sufficient condition for stability to supersonic disturbances and an estimate for the growth rate of an unstable supersonic disturbance are given.