A Theory of Deep Stratification and Overturning Circulation in the Ocean

A simple theoretical model of the deep stratification and meridional overturning circulation in an idealized single-basin ocean with a circumpolar channel is presented. The theory includes the effects of wind, eddies, and diapycnal mixing; predicts the deep stratification in terms of the surface forcing and other problem parameters; makes no assumption of zero residual circulation; and consistently accounts for the interaction between the circumpolar channel and the rest of the ocean. The theory shows that dynamics of the overturning circulation can be characterized by two limiting regimes, corresponding to weak and strong diapycnal mixing. The transition between the two regimes is described by a nondimensional number characterizing the strength of the diffusion-driven compared to the wind-driven overturning circulation. In the limit of weak diapycnal mixing, deep stratification throughout the ocean is produced by the effects of wind and eddies in a circumpolar channel and maintained even in the limit of vanishing diapycnal diffusivity and in a flat-bottomed ocean. The overturning circulation across the deep stratification is driven by the diapycnal mixing in the basin away from the channel but is sensitive, through changes in stratification, to the wind and eddies in the channel. In the limit of strong diapycnal mixing, deep stratification is primarily set by eddies in the channel and diapycnal mixing in the basin away from the channel, with the wind over the circumpolar channel playing a secondary role. Analytical solutions for the deep stratification and overturning circulation in the limit of weak diapycnal mixing and numerical solutions that span the regimes of weak to strong diapycnal mixing are presented. The theory is tested with a coarse-resolution ocean general circulation model configured in an idealized geometry. A series of experiments performed to examine the sensitivity of the deep stratification and the overturning circulation to variations in wind stress and diapycnal mixing compare well with predictions from the theory.