Figure 7 compares the convective pattern at a smaller Rayleigh number with that in figure 6. In the case of the smaller Rayleigh number shown in
Figure 7, only large convection cells exist. Since the modes at k~6
are stable when the Rayleigh number is small, only unstable modes with k~0
can grow and the corresponding convection cells emerge.
The structure of temperature disturbance observed in figure 7(b) is almost uniform
vertically, which is preferable for the approximation performed so far. However, as shown
in figure 7(a), convection at high Rayleigh numbers has a complicated temperature field in
the vertical direction. The behavior of convection obtained by the truncated system is
asssumed to have a larger quantitative error as the Rayleigh number increases.
Nevertheless, the qualitative features, for example, the emergence of small and large
horizontal scale convection cells, can be sufficiently expliained by the truncated system.
