The point of this paper is to compare many different diagnostics of mixing rates and to demonstrate the equivalence between Lagrangian diffusivities, passive tracer mixing, and the mixing of potential vorticity. The link to eddy potential vorticity fluxes is especially important because of the connection to the meridional overturning circulation. Although the flow is idealized, we hope this work can be useful in the context of the DIMES experiment. The results can be summarized by this figure, which compares the vertical profile of the different diagnostics.
Mesoscale eddies mix tracers horizontally in the ocean. This paper compares different methods of diagnosing eddy mixing rates in an idealized, eddy-resolving model of a channel flow meant to resemble the Antarctic Circumpolar Current. The first set of methods, the “perfect” diagnostics, are techniques suitable only to numerical models, in which detailed synoptic data is available. The perfect diagnostic include flux-gradient diffusivities of buoyancy, QGPV, and Ertel PV; Nakamura effective diffusivity; and the four-element diffusivity tensor calculated from an ensemble of passive tracers. These diagnostics reveal a consistent picture of along-isopycnal mixing by eddies, with a pronounced maximum near 1000 m depth. The only exception is the buoyancy diffusivity, a.k.a. the Gent-McWilliams transfer coefficient, which is weaker and peaks near the surface and bottom. The second set of methods are observationally “practical” diagnostics. They involve monitoring the spreading of tracers or Lagrangian particles in ways that are plausible in the field. We show how, with sufficient ensemble size, the practical diagnostics agree with the perfect diagnostics in an average sense. Some implications for eddy parameterization are discussed.