The GM plus E closure: A framework for coupling backscatter with the Gent and McWilliams parameterization

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.