Emergent eddy saturation from an energy constrained eddy parameterisation

•Emergent eddy saturation with an eddy parameterisation.•Eddy energy constrained eddy transfer coefficient.•Coupled to a prognostic parameterised total eddy energy budget.•Recipe for implementation in a general circulation model is proposed.

The large-scale features of the global ocean circulation and the sensitivity of these features with respect to forcing changes are critically dependent upon the influence of the mesoscale eddy field. One such feature, observed in numerical simulations whereby the mesoscale eddy field is at least partially resolved, is the phenomenon of eddy saturation, where the time-mean circumpolar transport of the Antarctic Circumpolar Current displays relative insensitivity to wind forcing changes. Coarse-resolution models employing the Gent-McWilliams parameterisation with a constant Gent-McWilliams eddy transfer coefficient seem unable to reproduce this phenomenon. In this article, an idealised model for a wind-forced, zonally symmetric flow in a channel is used to investigate the sensitivity of the circumpolar transport to changes in wind forcing under different eddy closures. It is shown that, when coupled to a simple parameterised eddy energy budget, the Gent-McWilliams eddy transfer coefficient of the form described in Marshall et al. (2012) [A framework for parameterizing eddy potential vorticity fluxes, J. Phys. Oceanogr., vol. 42, 539-557], which includes a linear eddy energy dependence, produces eddy saturation as an emergent property.