A New Look at Eddy Diffusivity as a Mixing Diagnostic

Abstract

It is shown that the Eulerian-mean advection?diffusion equation for a passive tracer, q, can be cast, uniquely and exactly into where the bar denotes an arbitrary Eulerian average (spatial, temporal, or both), v* is a nondivergent effective transport velocity, and K* is a scalar that varies in space and time. Furthermore, K* = Kk + Km, where Kk represents (possibly nonlocal) along-gradient dispersion of tracer isosurface, whereas represents local mixing due to diffusion at unresolved scales (D) amplified by resolved (but averaged) fluid dynamical stirring. The amplifying factor, |?q|2/|?q|2, measures local roughness of tracer field and determines the spatiotemporal structure of Km. This factor is called ?mixing efficiency? and it is proposed as a diagnostic of mixing. The mixing efficiency diagnostic is demonstrated using potential vorticity and nitrous oxide from the outputs of the Geophysical Fluid Dynamics Laboratory (GFDL) SKYHI general circulation model (GCM) analyzed on the 320-K isentropic surface for the month of March. It is found that mixing is severely suppressed along the jet axes at the midlatitude tropopause with marked zonal localization in the Northern Hemisphere. The formalism's relationship to the previously derived modified Lagrangian-mean theory is also discussed.