Figure 4 shows the aspect ratio of those convection cells that extend from beneath the plate to the outside with respect to the horizontal scale of the plate. The values of aspect ratio are completely different for the case of Ra=10^{4} from those of Ra=10^{5} or 10^{6}. In the case of Ra=10^{4}, the aspect ratio remains the same for all plate sizes. In the cases of Ra=10^{5} and 10^{6}, however, the aspect ratio of the convection cell increases as the horizontal size of the plate increases. Moreover, the horizontal scale of the cells tends to be almost the same as that of the plate, especially for the case of Ra=10^{5}. |
Figure 4: Aspect ratio of the convection cells obtained by numerical calculation. The vertical and horizontal axes represent the aspect ratio and the horizontal size of the plate, respectively. +: Ra=10^{6}, : Ra=10^{5}, : Ra=10^{4}. |
We can summarize the characteristics of the convection revealed by numerical calculations as follows.
- In all cases, a convection cell exists which has an upward flow beneath the plate and a downward flow outside the plate.
- However, the horizontal scale of the convection cell varies according to the Rayleigh number. When Ra=10^{4}, an upwelling exists beneath the margin of the plate, and the convection cell is rather narrow. However, when Ra=10^{5} or 10^{6} upwellings occur under the center of the plate and convection cells emerge that have extend from the center of the plate to the outside.