Statistical classification of flow morphology in rapidly rotating Rayleigh-B\'{e}nard convection: A numerical and experimental synthesis*

We use experimentally accessible statistical measures to distinguish between flow morphologies in rapidly rotating Rayleigh-B\'{e}nard convection (RRBC). Transitions between different flow regimes are identified for the fixed non-dimensional Prandtl number $\sigma = 7$ in terms of the reduced Rayleigh number $\widetilde{Ra}=RaE^{4/3}$, where $E$ is the non-dimensional Ekman number. Using cross-correlations of synthetic thermistor time signals we find that the flow transitions from the cellular regime to the convective Taylor column (CTC) regime at $\widetilde{Ra} \approx 20$, and from the CTC regime to the plume regime at $\widetilde{Ra} \approx 57$. Additionally, the horizontal flow structure is elucidated via spatial cross-correlations of vertically separated thermal fluctuations. Length, time, and velocity scales are produced for coherent columnar structures via spatial and temporal cross-correlations. Length, time and velocity scale data is seen to fit power-laws of the form $\alpha(\widetilde{Ra} - \widetilde{Ra}_{c})^{\beta}$, where $\widetilde{Ra}_c$ is the critical Rayleigh number for the onset of stationary convection. Through direct numerical simulation of non-hydrostatic quasi-geostrophic equations, a detailed examination of the flow morphology in RRBC is carried out.