Equatorially trapped convection in a rapidly rotating shallow shell

Motivated by the recent discovery of subsurface oceans on planetary moons and the interest they have generated, we explore convective flows in shallow spherical shells of dimensionless gap width epsilon(2) << 1 in the rapid rotation limit E << 1, where E is the Ekman number. We employ direct numerical simulation (DNS) of the Boussinesq equations to compute the local heat flux Nu(lambda) as a function of the latitude lambda and use the results to characterize the trapping of convection at low latitudes, around the equator. We show that these results are quantitatively reproduced by an asymptotically exact nonhydrostatic equatorial beta-plane convection model at a much more modest computational cost than DNS. We identify the trapping parameter beta = epsilon E-1 as the key parameter that controls the vigor and latitudinal extent of convection for moderate thermal forcing when E similar to s and epsilon down arrow 0. This model provides a theoretical paradigm for nonlinear investigations.