EDDY VISCOSITY AND STOCHASTIC BACKSCATTER PARAMETERIZATIONS ON THE SPHERE FOR ATMOSPHERIC CIRCULATION MODELS

Stochastic backscatter, eddy drain viscosity, and net eddy viscosity p arameterizations are formulated and calculated for two-dimensional tur bulence on the sphere based on eddy damped quasi-normal Markovian and direct interaction approximation closures. The net eddy viscosity is f ound to be the relatively small difference between the eddy drain visc osity and the backscatter viscosity. These eddy parameterizations have a cusp behavior at the cutoff wavenumber where they have their larges t magnitudes. Large-eddy simulations (LES) with the barotropic vortici ty equation have been performed incorporating these dynamic subgrid-sc ale parameterizations and compared with higher-resolution direct numer ical 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 nonr otating 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.