2-DIMENSIONAL SECONDARY INSTABILITIES IN A STRONGLY STRATIFIED SHEAR-LAYER

In a stably stratified shear layer, thin vorticity layers ('baroclinic layers') are produced by buoyancy effects and strain in between the K elvin-Helmholtz vortices. A two-dimensional numerical study is conduct ed, in order to investigate the stability of these layers. Besides the secondary Kelvin-Helmholtz instability, expected but never observed p reviously in two-dimensional numerical simulations, a new instability is also found. The influence of the Reynolds number (Re) upon the dyna mics of the baroclinic layers is first studied. The layers reach an eq uilibrium state, whose features have been described theoretically by C orcos & Sherman (1976). An excellent agreement between those predictio ns and the results of the numerical simulations is obtained. The baroc linic layers are found to remain stable almost up to the time the equi librium state is reached, though the local Richardson number can reach values as low as 0.05 at the stagnation point. On the basis of the wo rk of Dritschel et al. (1991), we show that the stability of the layer at this location is controlled by the outer strain field induced by t he large-scale Kelvin-Helmholtz vortices. Numerical Values of the stra in rate as small as 3% of the maximum vorticity of the layer are shown to stabilize the stagnation point region. When non-pairing flows are considered, we find that only for Re greater than or equal to 2000 doe s a secondary instability eventually amplify in the layer. (Re is base d upon half the initial vorticity thickness and half the velocity diff erence at the horizontally oriented boundaries.) This secondary instab ility is not of the Kelvin-Helmholtz type. It develops in the neighbou rhood of convectively unstable regions of the primary Kelvin-Helmholtz vortex, apparently once a strong jet has formed there, and moves alon g the baroclinic layer while amplifying. It next perturbs the layer ar ound the stagnation point and a secondary instability, now of the Kelv in-Helmholtz type, is found to develop there.We next examine the influ ence of a pairing upon the flow behaviour. We show that this event pro motes the occurrence of a secondary Kelvin-Helmholtz instability, whic h occurs for Re greater than or equal to 400. Moreover, at high Reynol ds number (greater than or equal to 2000), secondary Kelvin-Helmholtz instabilities develop successively in the baroclinic layer, at smaller and smaller scales, thereby transferring energy towards dissipative s cales through a mechanism eventually leading to turbulence. Because th e vorticity of such a two-dimensional stratified flow is no longer con served following a fluid particle, an analogy with three-dimensional t urbulence can be drawn.