Frictional effects on the deep-flow feedback on the ββ-drift of a baroclinic vortex over sloping topography

The propagation of compact, surface-intensified vortices on the ββ-plane is studied in the framework of a two-layer model with sloping topography. In contrast with previous work, we consider here bottom friction, modeled by an Ekman suction term. A perturbation theory is derived for a circular vortex in the upper layer with the lower layer at rest as a basic state. An integral momentum balance for the upper layer is used to obtain expressions for the velocity of the vortex center with the assumption that the interface is described by a circular dome in the leading order. This approach allows us to reduce the problem to the calculation of the deep-flow pattern, depending on the interface shape and bottom friction. The most essential parts of the deep-flow pattern are elongated dipolar gyres generated by the cross-slope ββ-drift. The corresponding deep-flow feedback provides an additional along-slope propagation, which is proportional to the cross-slope drift speed and to the ratio of the interface slope to the topographic slope. Over a steep topographic slope, when the lower layer depth contours are open, the deep flow approaches the inviscid solution in the limit of small friction. On the other hand, in the case of a gentle topographic slope, the inviscid limit does not exist on a certain set of closed contours of the lower layer thickness field, lying beneath the dome. In this case, the deep-flow pattern becomes strongly asymmetric and frictionally controlled; the dominant deep-flow circulation and corresponding coefficient of the deep-flow feedback are then inversely proportional to the friction coefficient. The results are compared with numerical simulations and observations.