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It is a well established result of linear theory that the influence ofdiffering mechanical boundary conditions, i.e., stress-free or no-slip, on theprimary instability in rotating convection becomes asymptotically small in thelimit of rapid rotation. This is accounted for by the diminishing impact of theviscous stresses exerted within Ekman boundary layers and the associatedvertical momentum transport by Ekman pumping. By contrast, in the nonlinearregime recent experiments and supporting simulations are now providing evidencethat the efficiency of heat transport remains strongly influenced by Ekmanpumping in the rapidly rotating limit. In this paper, a reduced model isdeveloped for the case of low Rossby number convection in a plane layergeometry with no-slip upper and lower boundaries held at fixed temperatures. Acomplete description of the dynamics requires the existence of three distinctregions within the fluid layer: a geostrophically balanced interior where fluidmotions are predominately aligned with the axis of rotation, Ekman boundarylayers immediately adjacent to the bounding plates, and thermal wind layersdriven by Ekman pumping in between. The reduced model uses a classical Ekmanpumping parameterization to alleviate the need for spatially resolving theEkman boundary layers. Results are presented for both linear stability theoryand a special class of nonlinear solutions described by a single horizontalspatial wavenumber. It is shown that Ekman pumping allows for significantenhancement in the heat transport relative to that observed in simulations withstress-free boundaries. Without the intermediate thermal wind layer thenonlinear feedback from Ekman pumping would be able to generate a heattransport that diverges to infinity. This layer arrests this blowup resultingin finite heat transport at a significantly enhanced value.

A nonlinear model for rotationally constrained convection with Ekman pumping