The Filtering Approach as a Tool for Modeling and Analyzing Turbulence

The Filtering Approach (FA) is a simple multiscale method of analysis, it extends the statistical formalism to a generic filtering operator and main ingredients are the Generalized Central Moments (GCM) homomorphic to the Statistical Central Moments (SCM). In the past this technique was intensively used to model turbulent flows in the context of the Large Eddy Simulation (LES) and at present is more and more applied to analyze turbulence and extract statistical data from under-resolved databases. In this paper we will briefly summarize the main multiscale characters of the FA, the well known identity relating GCM of the second order at different levels is discussed in detail, and a new identity relating GCM of the third order at different levels is presented. Finally some recent developments are illustrated. The structure of the subfilter stresses and the decomposition of the Reynolds stresses is examined, hybrid LES modeling procedures are applied and metrics that measure the statistical homogeneity of a turbulent flow are proposed.