Transient development of perturbations in a barotropic shear flow

Transient development of perturbations in a stratified zonal flow with a meridional shear is investigated. Use is made of closed form analytic solutions to study the two fundamental types of motion that were identified: Propagating gravity waves and pure vortex perturbations. Gravity waves grow transiently and may break in the neighborhood of a trapping plane where the intrinsic frequency of the waves reaches the Brunt-Väisälä frequency. Pure vortex perturbations exhibit a much larger growth associated with conservation in a straining field of perturbation vorticity. These two solution manifolds couple in the presence of strong shear or when the initial perturbation has a component varying strongly in the vertical and the energy growth attained by the vortex modes is transferred to the gravity waves. As a result, the perturbations attaining the greatest energy growth in the flow are combinations of vortex and gravity wave solutions producing regions with locally negative total density gradient that are expected to overturn.