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

We seek to develop a low-dimensional model for the interactions between horizontally adjacent turbulent convection rolls. This was tested in Rayleigh-Benard convection exper-iments with two adjacent cubic cells with a partial wall in between. Observed stable states include both counterrotating and corotating states for Rayleigh number 7.6 x 10(7) < Ra <3.5 x 10(9) and Prandtl number 6.41. The stability of each of these states and their dy-namics can be modeled low-dimensionally 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, which is projected onto the neighboring rolls with sinusoidal temperature profiles. With measurements of a constant coefficient for effective thermal turbulent diffusion, quantitative predictions are made for the nine forcing terms which affect stable fixed points of the corotating and counterrotating states for 5.5 x 10(8) < Ra <3.5 x 10(9). Predictions are found to be accurate within a factor of 3 of experiments. 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 corotating 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 corotating states. This temperature difference can be driven with an asymmetry, for example, by heating the plates of the two cells to different mean temperatures. When such an asymmetry is introduced, it also shifts the orientations of the rolls of counterrotating states in opposite directions away from their preferred orientation, which is otherwise due to the geometry of the cell. As the temperature difference between the plates of the different cells is increased, the shift in orientation increases until the counterrotating states become unstable and only corotating states are stable. At very large temperature differences between cells, both the counterrotating and predicted corotating states become unstable; instead we observe a corotating state with much larger temperature difference between the rolls that cannot be explained by turbulent thermal diffusion. Spontaneous switching between corotating and counterrotating states is also observed, including in nominally symmetric systems. Switching to counterrotating 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 corotating states is mainly driven by smaller diffusive fluctuations in the orientation, amplitude, and mean temperature of rolls, which have a positive feedback that destabilizes the counterrotating state.