Figure 11 compares our estimates of the maximum horizontal scales of convection cells with the results of numerical calculations. The horizontal size of the plate used in the numerical calculation is 6. The theoretical analysis indicates that horizontal scales of up to 2 will exist in the case of Ra=10⁴, whereas when Ra=10⁵,10⁶, convection cells of the same horizontal sizes as the plate can emerge. These analytical results are consistent with the results of the numerical calculations.

It is suggested that in cases of horizontally larger plates, convection cells with aspect ratios larger than 10 cannot emerge at Ra=10⁵. Thus, even under those conditions, upwelling will occur under the margins of the plates longer than 10.

Figure 11: Comparison between estimates of the maximum horizontal scales of convection cells and the results of numerical calculations.