Evaluating Diffusive Parameterizations of the Effects of Mesoscale Eddies based on Linear Stability Analysis

We diagnose the GM and isopycnal eddy diffusivities from a global eddying ocean model and compare them with predictions from linear stability analysis (LSA) using the wave with the largest growth rate. The buoyancy diffusivities are diagnosed from the baroclinic production term and are found to be negative in many parts of the Gulf Stream, Kuroshio Current and ACC and positive on their flanks.

The isopycnal diffusivities are diagnosed from Lagrangian particle dispersion of numerical particles in the model in both cross- and alongstream directions and are highly anisotropic. The Lagrangian integral time scale exhibits a maximum at the steering level predicted from linear theory where mean flow and phase speed of Rossby waves equal but the diffusivities decrease with depth, hence inconsistent with linear theory, because the eddy kinetic energy decays rapidly with depth. We explore the connection of GM and isopycnal diffusivities and the incorporation of a predictive model for eddy kinetic energy into the parameterization based on LSA.

The approach based on LSA is extended to include all waves and also wave propagation. This approach is based on the Rossby wave energy equation and includes the interaction of the waves with the mean flow. It allows for a non-diffusive closure for the effects of meso-scale eddies beyond Gent and McWilliams (1990).