Hallberg, R., and P. Rhines, 1996: Buoyancy-driven circulation in an ocean basin with isopycnals intersecting the sloping boundary. Journal of Physical Oceanography, 26(6), 913-940.

Abstract: The dynamics that govern the spreading of a convectively formed water mass in an ocean with sloping boundaries are examined using an isopycnal model that permits the interface between the layers to intersect the sloping boundaries. The simulations presented here use a two-layer configuration to demonstrate some of the pronounced differences in a baroclinically forced flow between the response in a basin with a flat bottom and vertical walls and a more realistic basin bounded by a sloping bottom. Each layer has a directly forced signal that propagates away from the forcing along the potential vorticity (PV) contours of that layer. Paired, opposed boundary currents are generated by refracted topographic Rossby waves, rather than Kelvin waves. It is impossible to decompose the flow into globally independent baroclinic and barotropic modes; topography causes the barotropic (i.e., depth averaged) response to buoyancy forcing to be just as strong as the baroclinic response. Because layer PV contours diverge, boundary currents are pulled apart at different depths even in weakly forced, essentially linear, cases. Such barotropic modes, often described as "caused by the JEBAR effect," are actually dominated by strong free flow along PV contours. With both planetary vorticity gradients and topography, the two layers are linearly coupled. This coupling is evident in upper-layer circulations that follow upper-layer PV contours but originate in unforced regions of strong lower-layer flow. The interior ocean response is confined primarily to PV contours that are either directly forced or strongly coupled at some point to directly forced PV contours of the other layer. Even when the forcing is strong enough to generate a rich eddy field in the upper layer, the topographic PV gradients in the lower layer stabilize that layer and inhibit exchange of fluid across PV contours. The dynamic processes explored in this study are pertinent to both nonlinear flows (strongly forced) and linear flows (weakly forced and forerunners of strongly forced). Both small (f plane) and large (full spherical variation of the Coriolis parameter) basins are included. Transequatorial basins, in which the geostrophic contours are blocked, are not described here.