  It is a well established result of linear theory that the influence of
differing mechanical boundary conditions, i.e., stress-free or no-slip, on the
primary instability in rotating convection becomes asymptotically small in the
limit of rapid rotation. This is accounted for by the diminishing impact of the
viscous stresses exerted within Ekman boundary layers and the associated
vertical momentum transport by Ekman pumping. By contrast, in the nonlinear
regime recent experiments and supporting simulations are now providing evidence
that the efficiency of heat transport remains strongly influenced by Ekman
pumping in the rapidly rotating limit. In this paper, a reduced model is
developed for the case of low Rossby number convection in a plane layer
geometry with no-slip upper and lower boundaries held at fixed temperatures. A
complete description of the dynamics requires the existence of three distinct
regions within the fluid layer: a geostrophically balanced interior where fluid
motions are predominately aligned with the axis of rotation, Ekman boundary
layers immediately adjacent to the bounding plates, and thermal wind layers
driven by Ekman pumping in between. The reduced model uses a classical Ekman
pumping parameterization to alleviate the need for spatially resolving the
Ekman boundary layers. Results are presented for both linear stability theory
and a special class of nonlinear solutions described by a single horizontal
spatial wavenumber. It is shown that Ekman pumping allows for significant
enhancement in the heat transport relative to that observed in simulations with
stress-free boundaries. Without the intermediate thermal wind layer the
nonlinear feedback from Ekman pumping would be able to generate a heat
transport that diverges to infinity. This layer arrests this blowup resulting
in finite heat transport at a significantly enhanced value.
