Upscale Energy Transfer in Three-Dimensional Rapidly Rotating Turbulent Convection

Rotating Rayleigh-Benard convection exhibits, in the limit of rapid rotation, a turbulent state known as geostrophic turbulence. This state is present for sufficiently large Rayleigh numbers representing the thermal forcing of the system, and is characterized by a leading order balance between the Coriolis force and pressure gradient. This turbulent state is itself unstable to the generation of depth-independent or barotropic vortex structures of ever larger scale through a process known as spectral condensation. This process involves an inverse cascade mechanism with a positive feedback loop whereby large-scale barotropic vortices organize small scale convective eddies. In turn, these eddies provide a dynamically evolving energy source for the large-scale barotropic component. Kinetic energy spectra for the barotropic dynamics are consistent with a k(-3) downscale enstrophy cascade and an upscale cascade that steepens to k(-3) as the box-scale condensate forms. At the same time the flow maintains a baroclinic convective component with an inertial range consistent with a k(-5/3) spectrum. The condensation process resembles a similar process in two dimensions but is fully three-dimensional.