Figure 12 compares our estimates of the maximum horizontal scales of convection cells with the horizontal scales of a supercontinent for the cases of whole and upper mantle convection.

In the case of whole-mantle convection, a supercontinent of approximately 20000 km width lying above a 2900 km-thick fluid layer is equivalent to scaled length of 7. The thickness of the plate is estimated to be 200-300 km on average if the tectosphere is included (Jordan, 1975), implying d=0.1. The value of the Rayleigh number is estimated to be 10⁶-10⁷ (e.g. Honda 1997). The figure illustrates that convection cells with the same horizontal scales as those of supercontinents can emerge, and that associated upwelling can be generated beneath the center of the plate.

In the case of upper mantle convection, the horizontal scale of a supercontinent in comparison with a fluid layer thickness of 670 km is about 30. In fact, this ratio is approximately 15 for the present-day Eurasian continent alone. The thickness of the plate is about d=0.3, and the pertinent value of the Rayleigh number approximately 6x10⁴-6x10⁵. In this case, the horizontal scale of the emergent convection cells is at most 10 for a plate of either scale. Consequently, an upwelling will emerge under the margins of the plate.

Figure 12: Comparison between estimates of the maximum horizontal scales of convection cells and the horizontal sizes of a supercontinent.