Stability of stratified shear flows (Q1064251)

For a steady plane parallel flow of an inviscid, incompressible fluid of variable density under gravity, it is shown that the complex wave velocity for any unstable mode lies in a semiellipse-type region whose major axis coincides with the diameter of Howard's semicircle, while its minor axis depends on the stratification. If \(kc_ i\) denotes the complex part of wave frequency and \(J_ 0\) the minimum of the local Richardson number over the flow domain, it is further established that \(kc_ i\to 0+\) as \(J_ 0\to 1/4-\). The case of free upper surface and conditional reduction dependent on the curvature of the basic velocity of the unstable region is also studied.