Dynamics of the Atlantic meridional overturning circulation. Part 1: Buoyancy-forced response

Abstract Historically, a hierarchy of ocean models have been used to investigate the dynamics of basin-scale, deep, meridional overturning circulations (MOCs). Near the base of this hierarchy are idealized solutions forced only by a surface buoyancy flux. Our goal is to provide a complete dynamical description of such “base” solutions, thereby placing the hierarchy on a firmer foundation. For this purpose, we obtain solutions to two types of models: a variable-density, layer ocean model (VLOM) and an ocean general circulation model (COCO), the former allowing for nearly analytic solutions and the latter for more accurate representation of processes. Solutions are obtained in an idealized, flat-bottom basin extending 40° in longitude and from the equator to 60°N, and for simplicity density depends only on temperature. Our standard runs are forced by a surface heating Q, which is spread uniformly throughout layer 1 in VLOM and at depths less than hmin in COCO; it quickly relaxes upper-ocean temperature to a prescribed T∗(y) that decreases linearly in the latitude band 30–50°N from 23 °C in the south to the temperature of the deep ocean, 3 °C, in the north. At the very bottom of our hierarchy are solutions to dynamically simplified versions of the models (i.e., no sub-mixed-layer entrainment or detrainment in VLOM, and no mixing and momentum advection in COCO) that adjust to a steady state without an MOC. Initially, Q forms an upper layer of thickness h1 = hmin and temperature T = T∗(y), and there is near-surface, eastward flow across the basin in the latitude band where Ty ≠ 0. At the eastern boundary, Kelvin waves cancel this current by adjusting h1 to a (nearly) parabolic profile he(y) that thickens poleward and eventually extends to the ocean bottom just south of 50°N. Subsequently, Rossby waves propagate across the basin, adjusting the solution to a state in which h1(x, y) = he(y) and T = T∗(y) above h1 everywhere in the basin. After this adjustment, the only remaining flows are zonally oriented, isopycnal, overturning cells within the upper layer, caused by thermal-wind shear in the latitude band where Ty ≠ 0. Our standard runs, which are solutions to the full models, necessarily adjust to a steady state with an MOC. Along and near the eastern boundary, Kelvin-wave adjustments still maintain the structure he(y), and Rossby waves begin to carry that structure offshore. Near 50°N, however, the Rossby waves are strongly damped. In VLOM, the damping is accomplished by a detrainment that prevents h1 from becoming larger than a prescribed maximum value. In COCO, it results primarily from horizontal diffusion, which thins h1 by cooling the deep ocean there. Because of the damping, there is an across-basin pressure gradient that drives northward geostrophic transport, forming the surface branch of the MOC; furthermore, the eastward-flowing MOC branch is located in a northern boundary layer where the damping is active. Because there is no wind forcing, there is no steady-state barotropic flow, and the deep response mirrors that in the upper layer. In most solutions, the upper and deep circulations are closed by diffusive upwelling mostly in the interior ocean and by downwelling primarily at the eastern boundary, the exceptions being for two of the extended solutions noted below. A useful aspect of VLOM is that it allows a closed, analytic expression for M ( H e ) , where M is the MOC transport and He is the eastern-boundary thermocline depth in the tropics. For realistic parameter choices, M is essentially proportional to H e 2 , in agreement with prior estimates based on ad hoc principles or determined empirically from numerical solutions. VLOM also provides an approximation for He(κ), where κ is the coefficient of vertical diffusion. Then, M [ H e ( κ ) ] describes the approximate dependency of M on κ, and it varies like κ 2 3 , again consistent with prior results. In COCO solutions, M exhibits similar dependencies on He and κ, a consistency traceable to he(y) being established in both systems by similar processes; however, the κ 2 3 relationship is not as precise because upwelling sources other than interior diffusion also contribute significantly to M . We also report four solutions that extend our standard runs in straightforward and insightful ways. They are solutions in which: (i) the MOC eastward branch is the surface flow of nearly isopycnal, nearly closed, thermal-wind cells that extend to the ocean bottom, a very different structure than for the northern boundary layer in the COCO standard run; (ii) T∗ depends on both x and y, and the MOC downwelling branch shifts to the northern boundary; (iii) Q is weakened enough to allow upper-layer temperature advection to impact the response; and (iv) the MOC upwelling branch is externally imposed by an exchange of water across the southern boundary of the basin. Despite the differences among these solutions and the standard runs, the underlying processes that generate the MOC and determine its strength remain unchanged, an indication that the MOC processes discussed here have general applicability.