Nonlinear ekman suction and ageostrophic effects in rapidly rotating flows

Abstract

Abstract A model is formulated to study the underlying dynamics of observed asymmetries in laboratory experiments on sidewall boundary layer separation and vertical shear layer instability in rapidly rotating fluids. These experiments show differences in transition behavior depending on the nature, cyclonic or anticyclonic, of the gyre forcing. Such qualitative signatures cannot be explained by the standard f-plane quasi-geostrophic model that is unaffected, apart from a switching of the flow direction, under changes of the sign of the forcing. An important ingredient of the intermediate model derived here is a nonlinear Ekman suction condition, which includes products of the interior velocity and its derivatives. The potential vorticity equation is closed using this nonlinear suction condition and other ageostrophic advections. For the case of a cylindrical, f-plane, barotropic ocean bounded by a vertical wall at r = L, and with a weak bottom slope, the nonlinear Ekman layers inhibit sidewall boundary la...