Convection at Ra=1.39x10⁴

The experiments at a Rayleigh number of 1.39 x 10⁴ are considered first. Isotherms in the projection data at this Rayleigh number (Figure 4.53) in the projections indicate the formation of longitudinal rolls in the fluid layer. For a cavity square in plan, the orientation of the rolls is indeterminate in principal, and will depend on mild imperfections in the experimental apparatus and non-uniformities in the thermal boundary condition. In the present work, the roll axis is seen to be parallel to the view angle. The rolls are stacked adjacent to one another, but the roll-width is not a constant. Despite the presence of a dominant flow pattern, the temperature field is fully three-dimensional, as can be seen from the lack of straightness of the isotherms in the projection. At the onset of longitudinal rolls in the fluid layer, scale analysis suggests the formation of as many rolls as the aspect ratio, 25 in the present experiment. The number of rolls seen in the projection data, Figure 4.39, is 15. The duration in the number of rolls with increase in Rayleigh number finds support in the work of Kolonder et al. [124]. These authors have reported a decrease in the number of rolls from 10 to 6 in a 10:5:1 cavity for a Rayleigh number increasing up to 2 x 10⁴.

The loss-of-roll phenomena has been predicted using stability theory and summarized in Figure 2 of Busse and Clever [118]. This figure indicates that the movement of the flow state occurs along the stability boundary that separates skewed varicose (SV) instability form the knot (KN) instability in a direction of diminishing wave- number. In the present set of experiments, the Rayleigh number was increased form zero to its final value is one step rather than in a gradual sequence. Hence the transitions that would occur for a gradual change in Rayleigh number were not visible in the fluid layer. Thus the appearance of 15 rolls (instead of 25, as should happen if equal-sized square rolls were to be formed) at Ra=1.39x10⁴ has been presented here, not as a transition point, but as a descriptor of the flow field.

Figure 4.53: Temperature surfaces in the cavity at three horizontal planes, Ra-1.39x10⁴,

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