Finite amplitude sideways diffusive convection

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Abstract
We consider the flow in a differentially heated vertical slot filled with a stably stratified solution. The stability of the flow driven by the differential heating is investigated in the limits of small but finite amplitude disturbances and very large solute Rayleigh number RS = gβ(∂Sa/∂z)D4/KSv. If the Schmidt number H = KT/KS is of order 1, the growth of an initial perturbation at the neutral point is balanced by horizontal advection of solute and heat, and a steady equilibration amplitude is attained. The Nusselt number is independent of all fluid properties and is directly proportional to the Rayleigh number excess ε = (Ra – Rac)/Rac. If H is much greater than |RS|⅙, or if the disturbance wave-number is slightly less than the critical wavenumber, subcritical instabilities are possible. In particular a resonant instability is possible. These theoretical predictions are consistent with previous experimental results and with the laboratory results described in this paper. In the experiments we find that the mixing of the initial sugar gradient is accomplished by convection cells which undergo transitions to larger wavelengths. The breakdown of the interfaces between convection cells is described.

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