TURBULENCE CLOSURES AND SUBGRID-SCALE PARAMETERIZATIONS

Recent developments in renormalized closure theory, including the generalization to inhomogeneous turbulence and its application for developing subgrid-scale parameterizations, are reviewed, focusing on two-dimensional and Rossby wave turbulence. Developments in the formulation and application of the quasi-diagonal direct interaction approximation (QDIA) closure for the interaction of general mean flows and topography with inhomogeneous two-dimensional and Rossby wave turbulence are discussed. It is also noted that for both homogeneous turbulence and inhomogeneous turbulence a regularization process in which transfers are localized in wavenumber space can overcome the small scale deficiencies of direct interaction approximation (DIA) type closures and that the localization parameter appears to be almost universal. For a wide range of large-scale Reynolds numbers and flow configurations there is in general very good agreement between the regularized DIA and QDIA closures and the statistics of DNS, except where sampling problems affect the DNS results (even with very large ensembles). The application of both DIA type closures and corresponding Markovianized versions for developing subgrid-scale parameterizations of renormalized viscosity and stochastic backscatter is discussed. Such parameterizations are needed for large-eddy simulations (LES) in which simulations are carried out at relatively coarse resolution to reduce computational costs and focus oil the large-scale features of the flows. Kinetic energy spectra of LES with dynamical subgrid-scale parameterizations have been found to compare closely with those of DNS at the scales of the LES.