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Oceanic mesoscale eddies are known to diffuse and stir tracers, and the development of skillful eddy closures is aided considerably by the accurate diagnosis of these processes from eddy‐resolving model statistics. In this work a multiple‐tracers inversion method is applied to a global mesoscale eddy‐resolving simulation, with the intent to solve for the eddy transport tensor that describes the eddy diffusion (symmetric part) and stirring (antisymmetric part). Special emphasis is placed on diagnosing the anisotropy of the horizontal transport, which is described by the eigenvalues and eigenvectors of the 2×2 horizontal symmetric subtensor. Global diagnoses of these quantities, along with an examination of their vertical structures, are used to recommend an algorithm for extending the Gent and McWilliams and Redi parameterizations to include anisotropic effects.

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This paper introduces two methods for dynamically prescribing eddy‐induced diffusivity, advection, and viscosity appropriate for primitive equation models with resolutions permitting the forward potential enstrophy cascade of quasi‐geostrophic dynamics, such as operational ocean models and high‐resolution climate models with O(25) km horizontal resolution and finer. Where quasi‐geostrophic dynamics fail (e.g., the equator, boundary layers, and deep convection), the method reverts to scalings based on a matched two‐dimensional enstrophy cascade. A principle advantage is that these subgrid models are scale‐aware, meaning that the model is suitable over a range of grid resolutions: from mesoscale grids that just permit baroclinic instabilities to grids below the submesoscale where ageostrophic effects dominate. Two approaches are presented here using Large Eddy Simulation (LES) techniques adapted for three‐dimensional rotating, stratified turbulence. The simpler approach has one nondimensional parameter, Λ, which has an optimal value near 1. The second approach dynamically optimizes Λ during simulation using a test filter. The new methods are tested in an idealized scenario by varying the grid resolution, and their use improves the spectra of potential enstrophy and energy in comparison to extant schemes. The new methods keep the gridscale Reynolds and Péclet numbers near 1 throughout the domain, which confers robust numerical stability and minimal spurious diapycnal mixing. Although there are no explicit parameters in the dynamic approach, there is strong sensitivity to the choice of test filter. Designing test filters for heterogeneous ocean turbulence adds cost and uncertainty, and we find the dynamic method does not noticeably improve over setting Λ = 1.