The Relationship between Large-Scale Flow Deformation and Mesoscale Eddy Anisotropy and Its Potential for the Parameterization of Eddy Effects

Mesoscale eddies are ubiquitous in the world ocean and have important impacts on large-scale ocean functioning that result from eddy transports of momentum, vorticity, heat and salt. Typically, these effects are not fully resolved in coupled climate models, and thus need to be prescribed based on properties of the larger-scale resolved flow. Motivated by an analogy between turbulence in Newtonian fluids and laminar flow in non-Newtonian fluids, Anstey and Zanna 2017 propose a parameterization of mesoscale eddy momentum fluxes based on the larger-scale flow deformation. Their parameterization implies a relationship between the deformation of the larger scale flow and the anisotropy of the smaller scale eddies. It raises many interesting questions about how large-scale flow deformation may influence eddy geometry and, by extension, eddy-mean flow feedbacks, and further whether this relationship can be effectively exploited in the parameterization of eddy effects. In this study, we aim to examine the parameterization proposed by Anstey and Zanna and its relationship to eddy flux geometry in an idealized model setting with two objectives: first, to examine the relationship between larger scale flow deformation and eddy flux anisotropy in a number of different dynamical regimes; and second, to develop insight into how best to implement the proposed parameterization that exploits this relationship. For the latter goal, we aim specifically to understand how best to define the optimal partition scale that separates the deformation-defining large-scale flow from the parameterization-targeting smaller scale eddying flow, and further how best to specify the eddy mixing rate that relates the parameterized eddy fluxes to the resolved deformation. Our examination is conducted using a well-studied quasi-geostrophic model of a two-dimensional, zonally-evolving, barotropically unstable jet. The model serves as an idealized representation of an oceanic western boundary current jet extension, like the Gulf Stream or Kuroshio Extension, downstream of where the current has separated from the coast. The model set-up has a number of advantages for this particular study: its eddy-mean flow interactions have been well-studied and are well understood; it contains a number of different eddy-mean flow interaction regimes; the nature of eddy-mean flow interactions can be systematically manipulated; and the model is inexpensive to run at spatial resolutions that well-resolve all relevant eddy scales. We find that both the nature of the large-scale flow deformation and small-scale eddy anisotropy are sensitive to the length scale chosen to partition the large- vs. eddy-scale flow, and further that the performance of the parameterization in predicting the fully-resolved eddy anisotropy is very sensitive to the partition scale. We suggest that the optimal partition scale (that which generates the closest agreement between the parameterization and the fully-resolved eddy anisotropy) varies with dynamical regime, and we show that the spatial patterns of both the optimal partition scale, as well as the optimal eddy mixing rate that acts in the parameterization as a constant of proportionality, display large-scale patterns that align with our dynamical understanding of this system. If one allows for local “tuning” of both the partition scale and eddy mixing rate, in general we can find a robust relationship between large-scale flow deformation and fully-resolved eddy anisotropy in most dynamical regimes, however there are some regions of the flow, such as inside the unstable jet, in which such a relationship appears inadequate. We suggest that large-scale flow deformation may thus be an important determinant of eddy anisotropy in some dynamical regimes but not others. On-going efforts focus on gaining a better understanding of the dynamical constraints that restrict when large-scale flow deformation is a good predictor of eddy anisotropy, and further of how the partition scale and eddy mixing rate, parameters that must be specified to implement the proposed parameterization, may themselves by informed by/parameterized by the resolved flow. Coarsely-resolved eddy kinetic energy shows promise as an informant for specifying these parameters, but more work is required to develop and test this proposal. REFERENCE: Anstey, J. and Zanna, L. (2017). A deformation-based parametrization of ocean mesoscale eddy Reynolds stresses. Ocean Modelling. 112. 10.1016/j.ocemod.2017.02.004.

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