Upscale Energy Transfer in Three-Dimensional Rapidly Rotating Turbulent Convection

Abstract

Rotating Rayleigh-Bénard 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.

Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers versus Interior Dynamics

“…An interesting feature of the GT regime is the formation of large-scale barotropic vortices driven by an upscale transport of kinetic energy [7,20]. The effect is most clearly observed in the stress-free case (Fig 3).…”

“…The formation of large scale vortices in rotating convection has recently been observed in simulations at larger E [21,22], where the large-scale energy accumulates predominantly in cyclonic structures. Such symmetry breaking is predicted to be absent in the asymptotic small Rossby number case [20]. Indeed, our DNS reveals the generation of both, strong cyclonic and anticyclonic vortices, which shows that symmetry slowly tends to be restored with decreasing Rossby number.…”

Laboratory-numerical models of rapidly rotating convection in planetary cores

“…Instead, we hypothesize that convection occurs in the form of 3-D geostrophic turbulence on smaller scales, whose energy then cascades upwards to larger-scale quasi-2-D flows (e.g. Mininni & Pouquet, 2010;Käpylä et al 2011;Chan & Mayr 2013;Favier et al 2014;Guervilly et al 2014;Rubio et al 2014;Stellmach et al 2014;Nataf & Schaeffer 2015), which are capable of efficiently generating observable magnetic fields. Ultimately, our findings suggest the need to revise current planetary dynamo models to include the effects of multiscale rotating convection dynamics and to determine how such flows produce planetary dynamo action.…”

Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

“…This ordering implies that the characteristic length and time scales of the magnetic fields will tend to exceed those of the thermal structures, which will again exceed the characteristic scales of the underlying flow fields, e.g., [10]). Indeed, energy is expected to be injected at small-scales via buoyancy-driven convection processes in natural dynamo systems ( [11][12][13]; Figure 1c), and is likely to then cascade upscale to larger scales [14], where we hypothesize that dynamo action likely occurs more efficiently [15] and where large-scale magnetic structures are likely formed. Thus, a detailed understanding of turbulent convection processes in metals is essential for the development of broadly accurate models of geophysical and astrophysical dynamo processes.…”