The large scale flow patterns driven by surface buoyancy flux are obtained as numerical solutions of the planetary geostrophic equations to which dissipation and diffusion have been appended. Within a cartesian β plane, square box geometry, the solution is made of gyres of the largest possible size with western and northern intensification, anticyclonic above the main thermocline, cyclonic below. Within regions of heat gain, the classical equilibrium between downward eddy diffusion and vertical upwelling is approximately observed in the main thermocline. As a consequence the abyssal circulation (southern interior and western boundary current) behave according to the early Stommel-Arons' ideas. The situation is rather different in regions of heat losses where convection is active: the flow patterns consist of swift zonal flows with horizontal divergence whose dynamics involve lateral diffusion of density and vorticity. The solutions are mostly sensitive to the choice of the vertical diffusion coefficient whose value between 1 and 2 cm2 s–1 produces realistic bottom water formation rates and meridional heat fluxes. The bulk of the heat accumulated in the Tropics is transported poleward by a direct Hadley cell (northward at the surface, southward at depth) obtained through a zonal averaging of the meridional circulation: horizontal rotational recirculations are less important for the heat transport.
de Verdière, A. C.. 1988. "Buoyancy driven planetary flows." Journal of Marine Research 46, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1887