The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard   convection
  Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are performed using an asymptotic quasi-geostrophic model that incorporates the effects of no-slip boundaries through (i) parameterized Ekman pumping boundary conditions, and (ii) a thermal wind boundary layer that regularizes the enhanced thermal fluctuations induced by pumping. The fidelity of the model, obtained by an asymptotic reduction of the Navier-Stokes equations that implicitly enforces a pointwise geostrophic balance, is explored for the first time by comparisons of simulations against the findings of direct numerical simulations and laboratory experiments. Results from these methods have established Ekman pumping as the mechanism responsible for significantly enhancing the vertical heat transport. This asymptotic model demonstrates excellent agreement over a range of thermal forcing for Pr ~1 when compared with results from experiments and DNS at maximal values of their attainable rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative agreement is achieved for Pr > 1. Similar to studies with stress-free boundaries, four spatially distinct flow morphologies exists. Despite the presence of frictional drag at the upper and/or lower boundaries, a strong non-local inverse cascade of barotropic (i.e., depth-independent) kinetic energy persists in the final regime of geostrophic turbulence and is dominant at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries, Ekman friction is found to attenuate the efficiency of the upscale energy transport and, unlike the case of stress-free boundaries, rapidly saturates the barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is strong enough to prevent the development of a coherent dipole vortex condensate. Instead vortex pairs are found to be intermittent, varying in both time and strength. 
Meredith Plumley, Keith Julien, Philippe Marti and Stephan Stellmach
physics.flu-dyn