Abstract :
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
