A new look at eddy diffusivity

A new diagnostic measure for local eddy diffusivity is proposed. The diagnostic is based on a rearranged Eulerian-mean equation for advection-diffusion. It is shown that the effective eddy diffusivity of a passive tracer q is

where D represents diffusion at unresolved scales whereas the bar denotes an average over finite time or space (or both). Keff accounts for the local irreversible transport of the tracer across its mean isosurface. Apart from the details in D, the structure of Keff is contained in the mixing efficiency

which measures the local geometrical complexity of the tracer field and reflects fluid dynamical stirring (tracer cascade). This diagnostic is closely related to the previously derived Lagrangian-mean effective diffusivity but defined in a coordinate system fixed on the Earth's surface.

Various quasi-conservative tracers (PV and N2O in the GFDL SKYHI GCM and a test tracer advected using the UKMO assimilated winds) are analyzed using the mixing efficiency diagnostic on a "middle-world" isentropic surface. Both spatial and temporal averages of varying degree reveal robust mixing barriers (i.e., minimum mixing efficiencies) along the jet axes at the midlatitude tropopause. The method successfully captures the zonally localized nature of the Northern Hemisphere barriers.