Flow reversals in turbulent convection with free-slip walls

We perform numerical simulations of turbulent convection for infinite Prandtl number with free-slip walls and study the dynamics of flow reversals. We show interesting correlations between the flow reversals and the nonlinear interactions among the large-scale flow structures represented by the modes (1, 1), (2, 1), (3, 1), and some others. After a flow reversal, the odd modes, e.g., (1, 1) and (3, 1), switch sign, but the even modes, e.g., (2, 2), retain their sign. The mixed modes (1, 2) and (2, 1) fluctuate around zero. Using the properties of the modes and their interactions, we show that they form a Klein four-group Z₂ × Z₂. We also show that for the free-slip boundary condition, the corner rolls and vortex reconnection are absent during a flow reversal, in contrast to active role played by them in flow reversals for the no-slip boundary condition. We argue that the flow reversals with the no-slip and free-slip boundary conditions are different because they are induced by nonlinearities (u ⋅ ∇)u and (u ⋅ ∇) θ, respectively.