Stability of stratified shear flows

AbstractFor 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 kci denotes the complex part of wave frequency and J0 the minimum of the local Richardson number over the flow domain, it is further established that kci → 0+ as J0 → 14−. The case of free upper surface and conditional reduction dependent on the curvature of the basic velocity of the unstable region is also studied