2. Theory

(TEk and TEddies), diapycnal mixing (TU) and northern sinking (TN). • The layer interface is pinned close to the surface at the southern boundary, to represent surface buoyancy loss and bottom water formation near Antarctica. • Forced by an idealized zonal wind jet near the circumpolar channel, with parameterized eddies (Gent & McWilliams,1990) and diapycnal mixing. • Experiments begin from an initial state with a flat shallow surface layer and no ACC. • The above figures show the evolution of surface layer thickness (closely related to circumpolar transport) in the numerical model and theory, for varying: (a) wind stress jet latitude, (b) wind stress magnitude, (c) eddy diffusivity, and (d) diapycnal diffusivity. The corresponding theoretical estimates are generally in good agreement with the numerical results. • The adjustment timescale (several centuries) is strongly influenced by the magnitude of the eddy diffusivity parameter. • With zero wind forcing (panel b), a circumpolar current still exists, driven by diapycnal mixing (see also Munday et al, 2011). • The grey lines in panel (a) show the theoretical estimate in which TEk is evaluated using the peak wind stress in the jet, rather than the mean wind stress over the circumpolar streamlines as suggested by Allison et al (2010). This leads to a reversal of the variation of the equilibrium pycnocline depth with wind stress latitude and an underestimate of the adjustment timescale. 1. Background information • Southern Ocean isopycnals are tilted steeply upwards towards Antarctica, and the baroclinic transport of the Antarctic Circumpolar Current (ACC) is linked to this meridional isopycnal slope. • Variations in the Southern Ocean wind stress drive ACC transport variability on interannual timescales, through the effect of Ekman pumping on the isopycnal slope (e.g., Hall and Visbeck, 2002) • The Southern Ocean’s response to wind stress changes on longer timescales is unknown, but is important for understanding the response of the global ocean to anthropogenic forcing, in terms of the oceanic uptake of carbon and the global ocean heat content. • Here we aim to understand the long-term adjustment of the ACC though its connection to the global pycnocline. Spin-up and adjustment of th