Stability of stratified flow with inhomogeneous shear

The temporal evolution of perturbations in stratified flow with inhomogeneous shear is examined analytically by an extension of the nonmodal approach to flows with inhomogeneous shear. The solutions of the equations that govern the linear evolution and the weak nonlinear evolution of perturbations of the stream function for stratified flow with monotonic inhomogeneous shear are obtained. It is shown that stabilization of perturbations arises from nonmodal effects due to flow shear. Conditions at which these nonmodal effects may be strong enough to stabilize the Rayleigh-Taylor instability are presented. These analytical results are also compared to numerical simulations of the governing equations performed by Benilov, Naulin, and Rasmussen