Abstract
For stratified compressible shear flows, it is shown that the instability region for subsonic disturbances is a semiellipse type region, which depends on the Richardson number, wave number, and depth of the fluid layer. If U( y) is the basic velocity, c = c r + ic i is the complex phase velocity, and J 0 the minimum of the local Richardson number, then this region reduces to the line c i = 0 when U′ min ≠ 0 and J 0 → 1 4 − in accord with Miles's theorem. Under an approximation, the role of curvature of the basic velocity profile on the stability of the flow is also studied.
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