Simulations with Pr=0.1
Asymmetric vs symmetric solutions

R=1.e7 - 34 frames

Ra=1.e7 Sampling rate: 0.001 thermal times / frame

R=1.e8 - 34 frames

Ra=1.e8 Sampling rate: 0.00033 thermal times / frame

At the beginning of the loop, the solution with R=1.e8 has the plume completely shifted toward the right, in a pattern not-too-dissimilar from the solution with R=1.e7. However, quite soon, the sweeping rightward current just below the surface creates a wave, and that evolves into a second plume, in a much more symmetrical position, which "takes the steam off" the original plume.

No such instability ever happens at R=1.e7. The b.l. current is probably not strong enough to make a new plume, but it is strong enough to keep the original plume in a shifted position. In the R vs. Nu graph, there is a bump in correspondence with the values of R having asymmetric solutions (that is R=1.e6 and R=1.e7).

Last update: 09/06/2003