A Recipe for Parametrizing Mesoscale Eddy Fluxes

Ocean mesoscale eddies strongly affect the strength and variability of large-scale ocean jets such as the Gulf Stream and Kuroshio Extension. Their horizontal scales, roughly 10 to 100 km, are too small to be adequately resolved in current ocean models. Representing eddy-mean flow processes in climate simulations remains a key challenge, especially quantifying the dependence of eddy effects on the underlying dynamics of the resolved flow and external forcing.

Here, we propose that the turbulent mesoscale eddy fluxes can be represented by resolved non-Newtonian (nonlinear) stresses. We diagnose the proposed relationship in idealized quasi-geostrophic and primitive equation models at different resolutions. We show that the closure could provide a successful parametrization of mesoscale eddies using only resolved and known quantities from the coarse-resolution model, such as velocity shear, stratification, coarse resolution grid-size, wind forcing and dissipation. We present a simple relationship between the closure and the ``eddy geometry'' representation of the Reynolds stress tensor.

The closure, when implemented in idealized model setups, leads to significant improvements in the mean and variability of the coarse-resolution parametrized simulations over the unparametrized versions. The effects of the parametrization are shown to allow for upgradient momentum fluxes, energy backscatter and enstrophy dissipation, therefore mimicking the eddy effects on the large-scale flow.