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The Gent and McWilliams (1990, GM) tracer transport scheme has long been a cornerstone of global-scale ocean modeling, and is well-known for its ability to mimic the effects of baroclinic turbulence by reducing the available potential energy of resolved flows. However, theory predicts that baroclinic turbulence also acts to transfer this potential energy to kinetic energy, which can then be fluxed toward larger scales by an inverse energy cascade. These dynamical processes represent a separate branch of the large-scale ocean energy cycle which GM presently does not account for. In this paper a framework is developed which allows the potential energy removed by the GM scheme to be transferred to resolved motions. In this framework, which is labeled GM+E (or "GM plus energetics"), the energy transfer occurs by employing GM alongside a parameterization of the barotropic Reynolds stresses in the momentum equations, which takes the form of a negative harmonic viscosity acting on the barotropic velocities. The Reynolds stress parameterization is considered as being complementary to GM, in that its energetics are explicitly tied to those of GM while being independent of the choice of transfer coefficient or form of the GM closure. A set of idealized baroclinic spindown simulations is used to compare GM+E against standard GM, and is shown to substantially improve the kinetic energy spectra, probability distributions of flow structures, and restratification rate within the front relative to an eddy-resolving truth simulation. • Mesoscale eddy closures should convert PE to KE, which is then cascaded upscale. • The energy extracted by the GM parameterization currently disappears from the model. • A closure for the barotropic Reynolds stresses is developed to complement GM. • "GM+E", the combined Reynolds stress and GM, closes the large scale energy cycle. • KE spectra and flow structures are improved by GM+E compared to standard GM. [ABSTRACT FROM AUTHOR]

A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier–Stokes- α model (LANS- α , e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS- α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ. [ABSTRACT FROM AUTHOR]