Rapidly Rotating Rayleigh-Benard Convection: Approaching the Asymptotic Limit of Quasigeostrophic Thermal Convection.

Current models and simulations of rotating fluid turbulence in the atmosphere and oceans, and planetary interiors are conducted in parameter regimes that are typically far removed from realistic values. Addressing this problem with present day models through improvements in computing power via Moore's law (giving a doubling of resolution in each direction every six years for three-dimensional problems) will produce slow advances at best. Advances may also occur through new model development and associated simulations utilizing extreme parameter values in an asymptotic manner. Such an approach will require a body of knowledge gained from large-scale direct numerical simulations and laboratory experiments that explore the nature of extreme values in controlled settings.

In this talk I will present and discuss results obtained from simulations of the asymptotic PDEs relevant for rapidly rotating Rayleigh-Benard convection. A particular strength of the reduced model PDE's is that they filter fast inertial waves and relax the need to resolve thin viscous (Ekman) boundary layers. This approach identifies four distinct flow morphologies (cellular convection, convective Taylor columns, plume convection and geostrophic turbulence) that remain challenging for laboratory experiments and DNS to capture in its entirety. Despite this challenge experiments and DNS offer an important benchmark for validation of the asymptotic theory. In comparison with laboratory experiments and DNS we show that the asymptotic model provides a good description of the fluid interior. However, in the presence of no-slip boundaries it is demonstrated that Ekman boundary layers can destabilize thermal boundary layers and result in significant enhancement in heat transport throughout the layer. We argue that this always occurs at some point on the rotationally constrained branch of thermal convection and thus of potential importance to geophysical and astrophysical scenarios. We show that the effect of Ekman pumping may be captured by classical pumping boundary conditions and again eliminates the need to resolve the Ekman boundary layer.