Interactions between two adjacent convection rolls in turbulent Rayleigh-Benard convection
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.