Parameterization of subgrid-scale non-linear transfers in quasi-geostrophic flows using direct numerical simulations

A generalization of the methodology outlined by Frederiksen and Kepert (2006) is used to calculate the eddy viscosity and stochastic backscatter for atmospheric and oceanic-like two-level quasi-geostrophic flows. The eddy viscosity and stochastic backscatter are formulated as matrices, with the diagonal entries representing horizontal transfers of energy (and enstrophy) and the off-diagonal entries representing vertical transfers. Both the isotropic formulation, where the eddy viscosities and backscatter depend only the total wavenumber, and the anisotropic formulation, where they depend on both total and zonal wavenumbers, are considered. Furthermore, truncations that resolve the internal radius of deformation scale, typical in atmospheric simulations, and those that do not, typical in oceanic simulations, are also considered. Kinetic energy spectra from low-resolution simulations employing the eddy viscosity and stochastic backscatter are found to be in good agreement with those obtained from high-resolution simulations.

REFERENCE

Frederiksen, J.S., and Kepert, S.M., 2006: Dynamical subgrid-scale parameterizations from direct numerical simulations, J.Atmos.Sci., 63, 3006-3019.