Stability of stratified compressible shear flows (Q1115258)

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 \(U'_{\min}\neq 0\) and \(J_ 0\to 1/4^-\) 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.