A Simple Two Dimensional Dynamical System for Eddy Saturation

James Roland Maddison, University of Edinburgh, School of Mathematics, Edinburgh, United Kingdom, David Philip Marshall, University of Oxford, Oxford, United Kingdom and Julian Mak, Hong Kong University of Science and Technology, Ocean Sciences, Hong Kong, Hong Kong
The reduced sensitivity of Southern Ocean zonal transport to surface wind stress changes, termed eddy saturation, has been observed in eddy permitting calculations, but may not be captured in lower resolution models with parametrized eddies. The GEOMETRIC scheme extends the Gent and McWilliams closure through the introduction of a specific dependence of the Gent-McWilliams coefficient on the total eddy energy, and couples this to a parametrized eddy energy budget. It has been found in numerical calculations in idealized configurations that this scheme is able to yield eddy saturation as an emergent property, arising from the interplay between mean momentum dynamics and eddy energetics.

Here a simple two dimensional dynamical system for the Southern Ocean is presented. The system is derived as a low dimensional reduced order model for a planetary geostrophic channel, subject to the GEOMETRIC form of the Gent and McWilliams closure, and coupled to a parametrized eddy energy budget. The fixed point of this system captures both eddy saturation and anti-frictional control mechanisms. Emergent dynamical time-scales, and the influence of stochastic momentum forcing on the dynamics, will be discussed.