Statistical Closure Theory and Subgrid-scale Parameterizations

Abstract
Recent developments in the formulation of turbulence closure theory for homogeneous and inhomogeneous turbulence and its application to the subgrid-scale parameterization problem are presented, focussing on two-dimensional turbulence. Non-Markovian closure models are compared with ensemble averaged direct numerical simulations (DNS) for decaying two-dimensional homogeneous turbulence. The application of the closures 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 on 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.

The quasi-diagonal direct interaction approximation (QDIA) closure theory for the interaction of mean flows, inhomogeneous turbulence, topography and possibly Rossby waves is presented and compared with DNS on f- and generalized beta- planes. Application of the QDIA closure to the parameterization of the eddy-topographic force is discussed.

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