Instabilities in variable-property flows, and the continuous spectrum
Seminar Room 1, Newton Institute
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.