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Abstract Eddy viscosity is employed throughout the majority of numerical fluid dynamical models, and has been the subject of a vigorous body of research spanning a variety of disciplines. It has long been recognized that the proper description of eddy viscosity uses tensor mathematics, but in practice it is almost always employed as a scalar due to uncertainty about how to constrain the extra degrees of freedom and physical properties of its tensorial form. This manuscript borrows techniques from outside the realm of geophysical fluid dynamics to consider the eddy viscosity tensor using its eigenvalues and eigenvectors, establishing a new framework by which tensorial eddy viscosity can be tested. This is made possible by a careful analysis of an operation called tensor unrolling, which casts the eigenvalue problem for a fourth‐order tensor into a more familiar matrix‐vector form, whereby it becomes far easier to understand and manipulate. New constraints are established for the eddy viscosity coefficients that are guaranteed to result in energy dissipation, backscatter, or a combination of both. Finally, a testing protocol is developed by which tensorial eddy viscosity can be systematically evaluated across a wide range of fluid regimes. 

Abstract Energy exchanges between large-scale ocean currents and mesoscale eddies play an important role in setting the large-scale ocean circulation but are not fully captured in models. To better understand and quantify the ocean energy cycle, we apply along-isopycnal spatial filtering to output from an isopycnal 1/32° primitive equation model with idealized Atlantic and Southern Ocean geometry and topography. We diagnose the energy cycle in two frameworks: 1) a non-thickness-weighted framework, resulting in a Lorenz-like energy cycle, and 2) a thickness-weighted framework, resulting in the Bleck energy cycle. This paper shows that framework 2 is more useful for studying energy pathways when an isopycnal average is used. Next, we investigate the Bleck cycle as a function of filter scale. Baroclinic conversion generates mesoscale eddy kinetic energy over a wide range of scales and peaks near the deformation scale at high latitudes but below the deformation scale at low latitudes. Away from topography, an inverse cascade transfers kinetic energy from the mesoscales to larger scales. The upscale energy transfer peaks near the energy-containing scale at high latitudes but below the deformation scale at low latitudes. Regions downstream of topography are characterized by a downscale kinetic energy transfer, in which mesoscale eddies are generated through barotropic instability. The scale- and flow-dependent energy pathways diagnosed in this paper provide a basis for evaluating and developing scale- and flow-aware mesoscale eddy parameterizations. Significance Statement Blowing winds provide a major energy source for the large-scale ocean circulation. A substantial fraction of this energy is converted to smaller-scale eddies, which swirl through the ocean as sea cyclones. Ocean turbulence causes these eddies to transfer part of their energy back to the large-scale ocean currents. This ocean energy cycle is not fully simulated in numerical models, but it plays an important role in transporting heat, carbon, and nutrients throughout the world’s oceans. The purpose of this study is to quantify the ocean energy cycle by using fine-scale idealized numerical simulations of the Atlantic and Southern Oceans. Our results provide a basis for how to include unrepresented energy exchanges in coarse global climate models. 

Abstract Mesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime. 

Abstract We use an interannually forced version of the Parallel Ocean Program, configured to resolve mesoscale eddies, to close the global eddy potential energy (EPE) budget associated with temperature variability. By closing the EPE budget, we are able to properly investigate the role of diabatic processes in modulating mesoscale energetics in the context of other processes driving eddy–mean flow interactions. A Helmholtz decomposition of the eddy heat flux field into divergent and rotational components is applied to estimate the baroclinic conversion from mean to eddy potential energy. In doing so, an approximate two-way balance between the “divergent” baroclinic conversion and upgradient vertical eddy heat fluxes in the ocean interior is revealed, in accordance with baroclinic instability and the relaxation of isopycnal slopes. However, in the mixed layer, the EPE budget is greatly modulated by diabatic mixing, with air–sea interactions and interior diffusion playing comparable roles. Globally, this accounts for ∼60% of EPE converted to EKE (eddy kinetic energy), with the remainder being dissipated by air–sea interactions and interior mixing. A seasonal composite of baroclinic energy conversions shows that the strongest EPE to EKE conversion occurs during the summer in both hemispheres. The seasonally varying diabatic processes in the upper ocean are further shown to be closely linked to this EPE–EKE conversion seasonality, but with a lead. The peak energy dissipation through vertical mixing occurs ahead of the minimum EKE generation by 1–2 months. 

Abstract The identification of vortices in a fluid flow is a dynamically interesting problem that has practical applications in oceanography due to the outsized role eddies play in water mass, heat, and tracer transport. Here a new Eulerian scheme is developed to detect both vortices and strongly strained fronts, which are both ubiquitous in the world ocean. The new scheme is conceptually linked to the well-known Okubo-Weiss parameter, but is extended to quasigeostrophic flows by recognizing the strong role played by vertical shear in ocean dynamics. Adapted from the λ 2 -criterion for vortex identification (Jeong and Hussain 1995), the scheme considers the curvature of the pressure field as the differentiator between vortical and strained flow structures, and it is shown that its underlying geometry also exhibits characteristics of quasigeostrophic flow. The uses and skill of the scheme are demonstrated using a high-resolution regional ocean simulation, and prospects for its use with observational products are discussed. 

The release of available potential energy by growing baroclinic instability requires the slope of the eddy fluxes to be shallower than that of mean density surfaces, where the amount of energy released depends on both the flux angle and the distance of fluid parcel excursions against the background density gradient. The presence of a lateral potential vorticity (PV) gradient is known to affect the growth rate and energy release by baroclinic instability, but often makes the mathematics of formal linear stability analysis intractable. Here the effects of a lateral PV gradient on baroclinic growth are examined by considering its effects on the slope of the eddy fluxes. It is shown that the PV gradient systematically shifts the unstable modes toward higher wavenumbers and creates a cutoff to the instability at large scales, both of which steepen the eddy flux angle and limit the amount of energy released. This effect may contribute to the severe inhibition of baroclinic turbulence in systems dominated by barotropic jets, making them less likely to transition to turbulence-dominated flow regimes.