## Abstract

Stochastic backscatter, eddy drain viscosity, and net eddy viscosity parameterizations are formulated and calculated for two-dimensional turbulence on the sphere based on eddy damped quasi-normal Markovian and direct interaction approximation closures. The net eddy viscosity is found to be the relatively small difference between the eddy drain viscosity and the backscatter viscosity. These eddy parameterizations have a cusp behavior at the cutoff wavenumber where they have their largest magnitudes.

Large-eddy simulations (LES) with the barotropic vorticity equation have been performed incorporating these dynamic subgrid-scale parameterizations and compared with higher-resolution direct numerical simulations (DNS), which are regarded as the benchmark or “truth” for comparisons. Good comparisons are found between kinetic energy spectra for the LES and the DNS at the scales of the LES for both nonrotating two-dimensional turbulence and differentially rotating Rossby wave turbulence. This is contrasted with much poorer comparisons when using a number of different ad hoc eddy viscosity parameterizations in LES.

*Corresponding author address:* Dr. Jorgen S. Fredriksen, CSIRO/DAR, Private Mail Bag 1, Aspendale, Victoria 3195, Australia.

Email: jsf@dar.csiro.au