  Rayleigh-B{\'e}nard convection experiments were done with two adjacent cubic
cells with a partial wall in between to force the generation of two interacting
convection rolls. Observed stable states include both counter-rotating and
co-rotating states. The stability of each of these states and their dynamics
were modeled by stochastic ordinary differential equations of motion in terms
of the orientation, amplitude, and mean temperature of each convection roll.
The form of the interaction terms is predicted based on an effective turbulent
diffusion of temperature between the adjacent rolls. Predictions are made for
stable fixed points of the co- and counter-rotating states. This suggests that
the same turbulent thermal diffusivity that describes macroscopically averaged
heat transport also controls the interactions between neighboring convection
rolls. The surprising stability of co-rotating states is due to the temperature
difference between the neighboring rolls becoming large enough that the heat
flux between the rolls stabilizes the temperature profile of aligned
co-rotating states. This temperature difference can be driven by heating the
plates of the two cells to different mean temperatures. This shifts the
orientations of the rolls of counter-rotating states in opposite directions,
and for large temperature differences only co-rotating states are stable
Spontaneous switching between co-rotating and counter-rotating states is also
observed. Switching to counter-rotating states occurs mainly due to cessation
(a significant weakening of a convection roll), which reduces damping on
changes in orientation, allowing the orientation to change rapidly due to
diffusive fluctuations. Switching to co-rotating states is mainly driven by
smaller diffusive fluctuations, which have a positive feedback that
destabilizes the counter-rotating state.
