Dynamics of the Atlantic meridional overturning circulation and Southern Ocean in an ocean model of intermediate complexity

A steady-state, variable-density, 2-layer, ocean model (VLOM) is used to investigate basic dynamics of the Atlantic meridional overturning circulation and Southern Ocean. The domain consists of idealized (rectangular) representations of the Atlantic, Southern, and Pacific Oceans. The model equations represent the depth-averaged, layer-1 response (except for one solution in which they represent the depth-integrated flow over both layers). To allow for overturning, water can cross the bottom of layer 1 at the velocity w(e) = w(d) + w(m) + w(n), the three parts representing: interior diffusion w(d) that increases the layer-1 thickness h throughout the basin, mixed-layer entrainment w(m) that ensures h is never less than a minimum value h(m), and diapycnal (cooling) processes external to the basin w(n) that adjust h to h(n). For most solutions, horizontal mixing has the form of Rayleigh damping with coefficient v, which we interpret to result from baroclinic instability through the closure, V* = -(v/f(2))del P, where del P = V (1/2g'h(2)) is the depth-integrated pressure gradient, g' is the reduced-gravity coefficient, and v is a mixing coefficient; with this interpretation, the layer-1 flow corresponds to the sum of the Eulerian-mean and eddy-mean (V*) transport/widths, that is, the "residual" circulation. Finally, layer-1 temperature cools polewards in response to a surface heat flux Q, and the cooling can be strong enough in the Southern Ocean for g' = 0 south of a latitude y(0), in which case layer 1 vanishes and the model reduces to a single layer 2. Solutions are obtained both numerically and analytically. The analytic approach splits fields into interior and boundary-layer parts, from which a coupled set of integral constraints can be derived. The set allows properties of the circulation (upwelling-driven transport out of the Southern Ocean M, down welling transport in the North Atlantic, transport of the Antarctic Circumpolar Current) and stratification (Atlantic thermocline depth, and the latitudes, y' and y(0), where h thins to h(m) or layer 1 vanishes in the Southern Ocean) to be evaluated in terms of model forcings (Southern-Ocean wind strength tau(a), Q, entrainment due to w(d)), processes (v, V* in the Southern Ocean, northern sinking, upwelling within the Atlantic Subpolar Gyre), and to the presence of the Pacific Ocean. A hierarchy of solutions is reported in which forcings and processes are individually introduced. The complete solution set includes a wide variety of solution types: with M > 0 and M <= 0; with and without wind forcing; with, without, and for two parameterizations of northern-boundary sinking that represent cooling external to and within the North Atlantic; for a wide range of v and tau(a); and for different closures. Novel aspects of the model and solutions include the following: use of VLOM, which allows Q. forcing to be introduced realistically; the aforementioned closure, which allows V* to be determined when layer 1 represents both the surface mixed layer (h = h(m)) and the depth of subsurface isopycnals (h > h(m)); latitude y', where layer 1 outcrops in the Southern Ocean, being internally determined rather than externally specified; and a boundary layer, based on Gill's (1968) solution, that smoothly connects the Southern- and Atlantic-Ocean responses across the latitude of the southern tip of South America. Finally, some solutions in the set are comparable to solutions to idealized, ocean general circulation models (OGCMs); in these cases, our solutions provide insight into the underlying dynamics of the OGCM solutions, for example, pointing toward processes that may be involved in eddy saturation and compensation. (C) 2016 The Authors. Published by Elsevier Ltd.