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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 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. 

Abstract The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive‐advective process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, diffusive contribution occurs mostly along the direction parallel to local neutral density surfaces. However, near the surface of the ocean, small‐scale turbulence and the presence of the boundary itself break this constraint and the mesoscale transport occurs mostly along a plane parallel to the ocean surface (horizontal). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive horizontal mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Horizontal fluxes are calculated on this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Horizontal diffusion can account for up to 10% of the total northward heat transport in the Southern Ocean and Western boundary current regions of the Northern Hemisphere. It also reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Finally, enabling horizontal diffusion leads to meaningful reductions in the near‐surface global bias of potential temperature and salinity. 

Abstract Tropical modes of variability, including the Madden‐Julian Oscillation (MJO) and the El Niño‐Southern Oscillation (ENSO), are challenging to represent in climate models. Previous studies suggest their fundamental dependence on zonal asymmetry, but such dependence is rarely addressed with fully coupled ocean dynamics. This study fills the gap by using fully coupled, idealized Community Earth System Model (CESM) and comparing two nominally ocean‐covered configurations with and without a meridional boundary. For the MJO‐like intraseasonal mode, its separation from equatorial Kelvin waves and the eastward propagation of its convective and dynamic signals depend on the zonal gradient of the mean state. For the ENSO‐like interannual mode, in the absence of the ocean's meridional boundary, a circum‐equatorial dominant mode emerges with distinct ocean dynamics. The interpretation of the dependence of these modes on zonal asymmetry is relevant to their representation in realistic climate models. 

Abstract Idealized models can reveal insights into Earth’s climate system by reducing its complexities. However, their potential is undermined by the scarcity of fully coupled idealized models with components comparable to contemporary, comprehensive Earth System Models. To fill this gap, we compare and contrast the climates of two idealized planets which build on the Simpler Models initiative of the Community Earth System Model (CESM). Using the fully coupled CESM, the Aqua configuration is ocean‐covered except for two polar land caps, and the Ridge configuration has an additional pole‐to‐pole grid‐cell‐wide continent. Contrary to most sea surface temperature profiles assumed for atmosphere‐only aquaplanet experiments with the thermal maximum on the equator, the coupled Aqua configuration is characterized by a global cold belt of wind‐driven equatorial upwelling, analogous to the eastern Pacific cold tongue. The presence of the meridional boundary on Ridge introduces zonal asymmetry in thermal and circulation features, similar to the contrast between western and eastern Pacific. This zonal asymmetry leads to a distinct climate state from Aqua, cooled by ∼2°C via the radiative feedback of clouds and water vapor. The meridional boundary of Ridge is also crucial for producing a more Earth‐like climate state compared to Aqua, including features of atmospheric and ocean circulation, the seasonal cycle of the Intertropical Convergence Zone, and the meridional heat transport. The mean climates of these two basic configurations provide a baseline for exploring other idealized ocean geometries, and their application for investigating various features and scale interactions in the coupled climate system.