The filtering approach as a tool for analyzing turbulence

The filtering approach was originally proposed by Leonard (1974) as a possible theoretical framework for the Large Eddy Simulation of turbulent flows. Today this technique is more and more applied to the analysis of turbulent flows. It mainly consists of a filtered representation of the turbulent flow at different filtering resolutions, and compared to the traditional multiscale techniques, Fourier, wavelets, POD, is very simple and intuitive. One drawback of the filtering approach, and in general of any decomposition technique, is the extension to inhomogeneous flows, due to the non commutivity of the filtering operator with the statistical average. A simple way to overcome this difficulty is to apply the partial statistical filtering procedure introduced by Yoshizawa (1982) in order to separate statistically the large scales from the subgrid scales. The practical implementation of this filter in LES modeling is very expensive, but its actuality as a tool for analyzing turbulence has to be remarked. In the contribution the Leonard and the Yoshizawa filtering approaches are compared and the peculiar properties of the latter are discussed in detail.