Eddy-Mean Flow Interaction With a Multiple Scale Quasi Geostrophic Model

Parameterization of mesoscale eddies in coarse resolution ocean models is necessary to include the effect of eddies on the large-scale oceanic circulation. We propose to use a multiple-scale Quasi-Geostrophic (MSQG) model to capture the eddy dynamics that develop in response to a prescribed large-scale flow. The MSQG model consists in extending the traditional quasi geostrophic (QG) dynamics to include the effects of a variable Coriolis parameter and variable background stratification. Solutions to this MSQG equation are computed numerically and compared to a full primitive equation model. The large-scale flow field permits baroclinically unstable QG waves to grow. These instabilities saturate due to non-linearities and a filtering method is applied to remove large-scale structures that develop due to the upscale cascade. The resulting eddy field represents a dynamically consistent response to the prescribed background flow, and can be used to rectify the large-scale dynamics. Comparisons between Gent-McWilliams eddy parameterization and the present solutions show large regions of agreement, while also indicating areas where the eddies feed back onto the large scale in a manner that the Gent-McWilliams parameterization cannot capture. Also of interest is the time variability of the eddy feedback which can be used to build stochastic eddy parameterizations.