The Stability of Stratified Jets

We study numerically the two dimensional linear instabilities of an incompressible, inviscid, density stratified, symmetric jet as a function of a width parameter, D. In the limit of infinite D, the maximum growth rate of temporal instability exponentially approaches that of the shear flow on either flank of the jet. The growth rate need not approach this limit monotonically, however. For some stratified flows it is possible that the odd (varicose) mode of a jet with sufficiently large width may grow more rapidly than the even (sinuous) mode. We also examine spatiotemporal instabilities of the Bickley profile, focusing specifically upon the identification of the regime of parameter space in which the flow is absolutely or convectively unstable. Finally, our methods of spatiotemporal linear stability analysis are applied to a more realistic asymmetric jet which mimics the internal wave related flow that develops in the lee of a topographic obstacle when “breaking” occurs. This analysis appears to bear strongly upon the interaction that occurs subsequent to wave breaking that leads to intense wave, mean-flow interaction.