HRT

Abstract

The stability work to be presented here is motivated by our ongoing numerical study of vortex merger in the presence of density-stratification. We find that very strong density stratification (even ``stable'' stratification) can (a) prevent the merger and (b) cause the vortices to break up. At low diffusivity levels the latter results from an inviscid instability due to alternately-signed density jumps packed in a known pattern. The analytical solution yields several co-existing unstable modes, and transient growth can add significantly to the linear growth at moderate times, thus speeding up the break-up of a single vortex. A related problem of Couette-Poiseuille flow and its continuous spectrum in the presence of low levels of base-flow vorticity will be discussed.