Eulerian and Lagrangian Isopycnal Eddy Diffusivities in the Southern Ocean of an Eddying Model

Lagrangian isopycnal diffusivities quantify the along-isopycnal mixing of any tracer with mean gradients along isopycnal surfaces. They are studied in the Southern Ocean of the 1/10 degrees Parallel Ocean Program (POP) model using more than 50 000 float trajectories. Concurrent Eulerian isopycnal diffusivities are estimated directly from the eddy fluxes and mean tracer gradients. Consistency, spatial variation, and relation to mean jets are evaluated. The diffusivities are calculated in bins large enough to reduce contributions from the rotational components that do not lead to net tracer mixing. Because the mean jets are nonzonal and nonparallel, meridional dispersion includes standing eddies and is significantly different from cross-stream dispersion. With the subtraction of the local Eulerian mean, the full Lagrangian diffusivity tensor can be estimated. Along-stream diffusivities are about 6 times larger than cross-stream diffusivities. Along-streamline averages of Eulerian and Lagrangian isopycnal diffusivities are similar in that they are larger north of the Antarctic Circumpolar Current (ACC) and smaller in the ACC in the upper 500 m. Eulerian diffusivities are often twice as large as the Lagrangian diffusivities below 500 m. There is large longitudinal variability in the diffusivities and in their relation to the mean flow. In bins with one prominent jet, diffusivities are reduced at the surface in the jet and increased to the north and south of the jet. There is a local maximum at depths of 500-1000 m. In other bins where mean jets merge and diverge because of topography, there is no consistent relation of the diffusivities with the mean flow. Eulerian fluxes are upgradient in about 15% of the bins.