Can convection cells evolve in stably stratified fluid?

Assume stably stratified fluid but not in equilibrium, e.g. with non-constant temperature gradient for example. Can convection cells be present? Typical example of convection cells is Rayleigh–Bénard convection. But this is example of unstably stratified fluid. In stably stratified fluid which is not in equilibrium is there some mechanism introducing instability? I'm targeting to low viscosity and very high externally-induced heat flux.

• Even under stable stratification, there can still be shear instability. The value if the Richardson Number is a criterium that takes care of this. – Dilaton May 25 '13 at 8:15
• The strength of the stratification plays a role in stability. If you look at the Richardson number Ri, N^2 (buyancy frequency) is in the numerator. Since one typical condition for shear instability is Ri < 0.25, that means that for lower values of N^2 the flow is more unstable than for higher values of N^2. – Isopycnal Oscillation May 25 '13 at 16:57
• @IsopycnalOscillation: I'm rather interested in situation where only buoyancy force acts on the fluid, thus excluding forced shear flow. I guess that in such a situation very high $N$ can induce turbulent instability but for mild $N>0$ fluid is led towards equilibrium slowly thus preserving stability. Do you agree? – Jan Blechta May 25 '13 at 18:22
• @JanBlechta I don't think a high N can induce turbulent instability, in fact, when N is high that means the gradient of the stratification is high and therefore turbulence is suppressed. What can happen is that a large N is conducive to internal waves which in turn are susceptible to shear and convective instabilities which may generate turbulence, but of course there needs to be some forcing mechanism. – Isopycnal Oscillation May 27 '13 at 2:56