Title: Dynamics of AMOC interactions with the Southern Ocean in a variable-density, two-layer model
An idealized, variable-density, 2-layer model is used to investigate basic dynamics of the AMOC and its interactions with the Southern Ocean. The model equations represent the layer-1 response (except for one solution in which they represent the depth-integrated flow). Horizontal mixing has the form of Rayleigh damping, which we interpret to result from baroclinic instability: Specifically, it results from a closure of the nonlinear terms in the continuity equation that sets the time-averaged eddy term, <h′v′>, to be proportional to the gradient of P = ½g′h2, where P is the depth-integrated pressure, h is the layer thickness, and g′ is the reduced-gravity coefficient; the layer-1 velocity field then corresponds to the “residual circulation,” that is, the Eulerian-mean plus eddy-mean flows. Water can flow across the bottom of layer 1, thereby allowing for the possibility of an overturning circulation. Finally, layer-1 temperature cools polewards in response to a surface heat flux, Q, which can be strong enough in the Southern Ocean for g′ = 0 south of a latitude y0, so that layer 1 vanishes there and the model reduces to a single layer 2. Solutions are found in idealized domains that include the Atlantic, Southern and Pacific Oceans, and are forced by x-independent wind-stress τx and Q fields. They are obtained both numerically and analytically. In the analytic approach, fields are split into interior and boundary-layer parts from which a coupled set of integral constraints is derived. Solutions to the set then relate integral properties of the AMOC and Southern Ocean to model forcings and processes. The model allow for a rich suite of solutions that represents well a variety of solutions to idealized, ocean general circulation models (OGCMs).