TRANSIENT DEVELOPMENT OF PERTURBATIONS IN STRATIFIED SHEAR-FLOW

Transient development of perturbations in inviscid stratified shear fl ow is investigated. Use is made of closed form analytic solutions that allow concise identification of optimally growing plane-wave solution s for the case of an unbounded flow with constant shear and stratifica tion. For the case of channel flow, variational techniques are employe d to determine the optimally growing disturbances. The maximum energy growth attained over a specific time interval decreases continuously w ith increasing stratification, and no special significance attaches to Ri = 0.25. Indeed, transient growth can be substantial even for Ri = O(1). A general lower bound on the energy growth attained by an optima l perturbation in a stratified flow over a given time interval is the square root of the growth attained by the corresponding perturbation i n unstratified flow. Enhanced perturbation persistence is found for me an-flow stratification lying in the range 0.1 < Ri < 0.3. Small but fi nite perturbations in mean flow with Ri < 0.4 produce regions with loc ally negative total density gradient, which are expected to overturn. Although the perturbations are of wave form, buoyancy fluxes mediate t ransfer between perturbation kinetic and potential energy during trans ient development, thus implying that buoyancy flux is not a determinat ive diagnostic for distinguishing between waves and turbulence in stra tified flows.