The effects of eddies in a primitive equation ocean model configured in a single hemisphere domain with circumpolar channels at their poleward ends are investigated; in particular, two regimes for the mass balance in the channel are investigated. With small overlying winds, the channel stratification is largely set by diffusion operating in the gyre portion of the domain: the depth scale varies with a fractional power of the diffusivity but has little dependence on the wind stress. As the winds are increased, the depth becomes increasingly controlled by a tendency toward small residual circulation. In this limit, a scaling theory is derived for the stratification in the channel that predicts the overall depth of the thermocline as a power of the wind stress and that allows the eddy length scale to differ from the channel length scale. The predicted depth depends on the details of the closure chosen for the eddy buoyancy flux, but in general it varies as some fractional power of the wind stress, and a channel-only numerical simulation agrees well with this prediction. When a gyre region is added to the channel, vertical diffusion in the gyre exerts some control on the channel stratification even at higher winds, forcing the mass balance into a mixed regime in which both eddy and diffusive effects are important. The depth scale varies less with the wind stress than in a channel-only configuration, and the residual mean circulation in the channel is maintained by the convergence of cross-isopycnal eddy buoyancy fluxes.
