Retrograde rotation of the large-scale flow in turbulent rotating Rayleigh-Benard convection with high Rossby number

We present measurements of the azimuthal orientation $\theta(t)$ of the large-scale circulation (LSC) for turbulent Rayleigh-B\'enard convection in the presence of week rotations ${\Omega}$. Linear retrograde rotations of the LSC circulating plane are observed over the entire Rossby-number range (1${\le}Ro{\le}$300) studied. When the $Ro$ increases, the ratio of the retrograde rotation rate, $\gamma=-{\langle}\dot{\theta}{\rangle}/{\Omega}$ remains nearly a constant $0.12$ in the range of (1${\le}Ro{\le}$80) and starts to increases when $Ro>80$. When $Ro{\simeq}300$, $\gamma$ approaches a value of $0.36$ close to the prediction from previous theoretical models. In a background of linear rotations, erratic changes in $\theta(t)$ accompanied by decreasing in the LSC amplitude $\delta$ are observed. These small-$\delta$ events give rise to the increasing $\gamma$ with very high Ro numbers (80${\le}Ro{\le}$300). In this range, the diffusivity of $\theta$ is proportional to $\delta^{-2}$. Moreover, the occurrence frequency of the small-$\delta$ events, and their average duration are independent on $Ro$. We propose a model to include additional viscous damping for the LSC azimuthal motion due to turbulent viscosity and provide theoretical interpretations of the experimental results.