This paper studies the impact of topography and increased vertical resolution on steady-state wind and buoyancy-driven circulation in the Subtropical Gyre. Buoyancy driving is represented by mass exchange across the interface separating layers of constant density. The mass exchange in turn is parameterized in terms of the departure of a layer thickness from a reference value. A 2-layer ocean model is developed that incorporates topography that depends on the meridional co-ordinate, and the problem reduces to solving a first order partial differential equation governing the upper layer inverse planetary potential vorticity. Two distinct families of characteristic curves are required to span the entire subtropical gyre; an "interior family" emanating from the eastern boundary and a family lying in the northwestern corner that begin and end along the oceanic edge of the western boundary current. It is demonstrated that when the ocean shoals (deepens) poleward, the area of the recirculating gyre in the northwestern corner decreases (increases) in response to the increased (decreased) phase speed of long baroclinic Rossby waves. The model is applied to the subtropical North Atlantic gyre, using climatological Ekman pumping, zonally averaged topography and a realistic representation of the eastern boundary and the solutions are qualitatively compared with these from a general ocean circulation model. To address how increased vertical resolution modifies the recirculating gyre structure, solutions are calculated for a 3-layer flat bottom ocean model. The circulation in the top and bottom layers of this model are qualitatively similar to those in the 2-layer model. In the middle layer there is a recirculating anticyclonic gyre of extent similar to that in the 2-layer model. Outside this gyre is a second anticyclonic gyre of larger horizontal extent. The double-gyre structure in the middle layer is associated with the existence of two separatrices subdividing the layers into three regions. These curves separate two distinct families of characteristic curves each associated with the upper and lower layer inverse planetary potential vorticity equations.