Diagnosing ocean eddy diffusivities from eddy flux divergences

Large-scale numerical ocean models typically include parametrizations for mesoscale eddies, and these are often based upon the principle of down-gradient mixing. The corresponding eddy diffusivities, when diagnosed directly from eddy fluxes, are generally polluted by the presence of large dynamically inert rotational components which require filtering. Here, instead, a new methodology is proposed, which constructs an inverse problem for eddy diffusivities in a manner which is independent of any rotational fluxes. This alleviates the aforementioned problems, diagnosing the diffusivity in a non-local, gauge-invariant fashion. This new diagnostic approach is applied to multi-layer quasi-geostrophic ocean gyre simulations, in order to diagnose eddy potential vorticity diffusivities. It is found that, away from the layer of direct wind forcing, the diffusivity is predominantly positive and has a significant degree of correlation with the eddy energy. The diagnostic approach is additionally applied to down-gradient buoyancy mixing, where both strong positive and negative diffusivity signals are observed. The consequences for eddy parametrizations are considered.