Statistical classification of flow morphology in rapidly rotating Rayleigh-Bénard convection

Abstract

In rapidly rotating convection four flow regimes with distinct characteristics have been identified via simulations of asymptotically reduced equations as a function of a reduced Rayleigh number RaE4/3 and Prandtl number σ (K. Julien, A. Rubio, I. Grooms, and E. Knobloch, “Statistical and physical balances in low Rossby number Rayleigh-Bénard convection,” Geophys. Astrophys. Fluid Dyn. 106, 392–428 (2012)). In each regime the flow organizes, with varying intensity, into coherent vertical structures. The identified morphologies, in order of increasing RaE4/3, consist of the cellular regime, the convective Taylor column regime, the plume regime, and a regime characterized by geostrophic turbulence. Presently, physical limitations on laboratory experiments and spatio-temporal resolution challenges on direct numerical simulations of the incompressible Navier-Stokes equations inhibit an exhaustive analysis of the flow morphology in the rapid rotating limit. In this paper the flow morphologies obtained from simulations of the reduced equations are investigated from a statistical perspective. We utilize auto- and cross-correlations of temporal and spatial signals that synthesize experimental data obtained from thermistor measurements or particle image velocimetry. We show how these statistics can be employed in laboratory experiments to (i) identify transitions in the flow morphology, (ii) capture the radial profiles of coherent structures, and (iii) extract transport properties of these structures. These results provide a foundation for comparison and a measure for understanding the extent to which rotationally constrained regime has been accessed by laboratory experiments and direct numerical simulations.