Simulations with Pr=0.1
Asymmetric vs symmetric solutions
R=1.e7 - 34 frames
Sampling rate: 0.001 thermal times / frame
R=1.e8 - 34 frames
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).