A flow model that integrates all aspects of the temperature contours is shown in a schematic diagram in Figure 4.59. This Figure shows the hot mass of fluid rising in the form of a buoyant fountain form the center of the four adjacent cells and distributing the cold fluid in the four quadrants from above, almost symmetrically. When viewed from any direction this flow field will show a roll-like repeating structure. The plume cross-section is not seen to be of any definite shape, but is closer to an ellipse than a circle. This is simply because the cubic cell has unequal edges.

Figure 4.58: Isotherm in the cavity at three horizontal planes, Ra=4.02 x 10⁴,

At a Rayleigh number 4.02 x 10⁴, the average dimensionless wave-number of the dominant roll-pattern was found to be 2.52. The stability diagram of Busse and Clever [118] does not extend beyond Ra = 2 x 10⁴. However, an examination of the stability diagram for Pr=7 (water) is possible though it is known that a higher Prandtl number has a stabilizing effect. The point falls very close to the cross-roll stability boundary. The corresponding shadowgraph images are vividly shown by Busse and Clever [118], and Nasuno et al. [117].

The work of Busse and Clever [118] shows that the approach to cross-rolls in water is via skewed varicose and knot instabilities as the Rayleigh number is raised. In contrast, at Pr =0.7 the sequence is skewed varicose, oscillatory, and with knot instabilities, but no data is really available for Ra> 15000. As discussed below, Lipps [127] has shown the formation of (semi) cross-rolls at Ra =2.5 x 10⁴ in a small aspect ratio fluid layer. The formation of cubic cells as dominant pattern, and a switch between this pattern and longitudinal rolls have been observed at Ra =4.02 x 10⁴ in the present experiments. This suggests that the boundaries of the oscillatory, knot, and cross-roll regimes (when extended) should be in the vicinity of this Rayleigh number in air. As in the case with Ra =1.39x10⁴, one cannot comment on the route followed in the present experiments by the flow field to attain its final state on the stability diagram.