Re-orientations of the large-scale circulation in turbulent Rayleigh-B{\'e}nard convection

We present measurements of the orientation $\theta_0(t)$ of the large-scale circulation (LSC) of turbulent Rayleigh-B{\'e}nard convection in cylindrical cells of aspect ratio 1. The orientation undergoes irregular reorientations. It contains two types of reorientation events to be called rotation and cessation. Rotation through angles $\Delta \theta$ has a monotonically decreasing probability distribution $p(\left| \Delta \theta \right|) \propto \left| \Delta \theta \right|^{- \gamma}$ with $\gamma \simeq 4$ reminiscent of heavy-tail distributions in many other systems. Cessations involve a brief vanishing of the LSC, followed by a new spontaneous re- organization of the LSC with a randomly chosen new orientation. Thus the probability distribution for cessation is uniform: $p( \left| \Delta \theta \right|) = 1/\pi$. Both rotations and cessations have Poissonian statistics in time.