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. $(1,1), (3,1)$, 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 $Z_2 \times Z_2$. 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 $ ({\bf u} \cdot \nabla) {\bf u}$ and $({\bf u} \cdot \nabla) \theta$ respectively.