Can Eulerian Eddy Diffusivity Be Inferred From Lagrangian Trajectories?

Abstract Lagrangian particle trajectories are widely used to characterize tracer dispersion and mixing driven by mesoscale currents (“eddies”), leading to estimates of eddy diffusivity that can in turn be used in non‐eddy‐resolving and eddy‐permitting ocean models. These Lagrangian estimates, however, are asymptotic quantities and cannot capture spatial and temporal variability in the eddy‐driven mixing. This study explores the use of Lagrangian particles to calculate the local (“Eulerian”) characteristics of tracer distribution and evolution in eddying flows, including tracer concentrations, eddy‐driven tracer fluxes and diffusivities. 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 can then be readily generated from a single realization of Lagrangian trajectories. Using an idealized eddy‐resolving double‐gyre ocean model, we found that these hybrid estimates closely match the direct, tracer‐based estimates, as long as the density of spatial particle coverage is sufficiently high. Specifically, the estimates are reliable until the particles' resolution decreases to about one particle per the first deformation radius. The proposed approach to estimating Eulerian eddy transport properties from Lagrangian particle trajectories may serve as a strong motivation for conducting Lagrangian field experiments with large particle ensembles.