Zonal flow reversals in two-dimensional Rayleigh-Bénard convection

Using long-time direct numerical simulations, we analyse the reversals of the large scale zonal
flow in two-dimensional Rayleigh–B´enard 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
behaviour, 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 characterised by a bimodal PDF of the largest scale mode, where
the flow fluctuates only between two distinct states with zonal flow travelling in opposite directions.