Eulerian eddy diffusivity is the key to eddy parameterization in non-eddy-resolving and eddy-permitting ocean models and quantifies locally the impact of inhomogeneous eddy-induced mixing. Practically, Lagrangian particle trajectories are widely used to characterize dispersion and mixing driven by eddies and large-scale currents. These Lagrangian estimates, however, are nonlocal in that they are diagnosed asymptotically and quantify the statistics of flows over a wide range of space and time. This study explores the use of such particles to calculate the local Eulerian properties of tracer distribution in eddying flows, including tracer concentration, eddy tracer flux, and Eulerian eddy diffusivity. The proposed "hybrid' Eulerian-Lagrangian approach assumes that continuous tracer evolutions can be described by motions of a finite number of fluid particles (parcels). Multiple tracer realizations are generated from a single realization of Lagrangian trajectories, by assigning different initial tracer contents to particles. Using an idealized eddy-resolving double-gyre ocean model, we found that these hybrid estimates closely match its Eulerian counterpart, as long as the number of particles is sufficiently high. Specifically, the estimates are reliable until the particles' resolution decreases to about one particle per deformation radius. The hybrid eddy diffusivity has a zonal-mean structure generally close to the Eulerian one. The remaining bias is noticeable in the vicinity of the western boundary current extension, which is explained by the inherent difference between the Lagrangian and Eulerian simulations. This study, for the first time, developed a feasible and efficient approach to estimating Eulerian eddy transport properties from ensembles of Lagrangian-particle trajectories.
Lu et al. (Mon,) studied this question.