Tanny, J. and Tsinober, A. (1988)
The dynamics and structure of double-diffusive layers in side wall heating experiments, Journal of Fluid Mechanics, 196, pp.135-156

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ABSRACT
The dynamics and structure of double-diffusive layers were studied experimentally by heating a linear stable solute gradient from a sidewall in a wide tank. The formation and subsequent development of the layers were investigated by various flow visualization techniques, namely, fluorescent dye, fluorescent particles and shadowgraph. Experiments were performed in order to determine the stability diagram of the flow, following in each experiment the phase trajectory of the system in the phase plane of thermal and solute Rayleigh numbers. The experimentally obtained stability diagram appears to be similar to that obtained numerically by Thangam et al (1981) and by Hart (1971) for a vertical narrow slot and a steady basic flow. It is shown that if the temperature of the sidewall rises slowly to its prescribed value, the thickness of the initial layers, formed at the onset of instability, is a function of the ambient density gradient and fluid properties only. On the other hand, if the wall temperature rises quickly (almost impulsive heating), the thickness of the initial layers is proportional to the imposed temperature difference, provided that the Rayleigh number, based on this difference, is larger than some critical value which is associated with the first merging of the layers. A criterion for the first merging of the initial layers is obtained, and it is suggested that this merging is due to subsequent instability of the system. The subsequent merging process, following the first merging, is not a simple successive doubling of the layer thickness and in each of five nearly identical experiments a different dependence of the average layer thickness on the instantaneous Rayleigh number is obtained. This indicates that the system of layers behaves chaotically after the first merging. The final thickness of the layers depends on the prescribed lateral temperature difference, and the ratio between the final and initial thickness of the layers is a linear function of the final Rayleigh number. Flow visualization experiments indicate that the layers consist of vortices with vertical scale of the layer thickness and various horizontal scales.

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