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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...