Zonal flow reversals in two-dimensional Rayleigh-Bénard convection

Using long-time direct numerical simulations, we analyze the reversals of the large scale zonal flow in two-dimensional Rayleigh-Bénard convection with a rectangular geometry of aspect ratio Γ. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, large scale flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, transitions are seen in the probability density function (PDF) of the largest scale mode. For Γ=2, the PDF first transitions from a Gaussian to a trimodal behavior, signifying the emergence of large scale flow reversals, where the flow fluctuates between three distinct states: two states in which a zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for Γ=1, the zonal flow reversals are characterized by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct states with zonal flow traveling in opposite directions.