On bifurcations of stratified shear flows

We consider the non-linear problem on the pairs of horizontal weakly-stratified shear flows which posses predicted fluxes of mass, momentum and energy. Using the methods of the branching theory, we reduce this problem to an equivalent system of implicit algebraic equations. Analysis of the branching system yields necessary and sufficient conditions for bifurcation of conjugate flows. As an example, we show numerically that these conditions are satisfied for a basic continuously stratified flow with a density profile being close to the two-layer stratification.