We live in a turbulent world observed through coarse-grained lenses. Coarse graining (CG), however, is not only a limit but also a need imposed by the enormous amount of data produced by modern simulations. Target audiences for our survey are graduate students, basic research scientists, and professionals involved in the design and analysis of complex turbulent flows. The ideal readers of this book are researchers with a basic knowledge of fluid mechanics, turbulence, computing, and statistical methods, who are disposed to enlarging their understanding of the fundamentals of CG and are interested in examining different methods applied to managing a chaotic world observed through coarse-grained lenses.

We live in a turbulent world observed through coarse-grained lenses. Coarse graining (CG), however, is not only a limit but also a need imposed by the enormous amount of data produced by modern simulations. Target audiences for our survey are graduate students, basic research scientists, and professionals involved in the design and analysis of complex turbulent flows. The ideal readers of this book are researchers with a basic knowledge of fluid mechanics, turbulence, computing, and statistical methods, who are disposed to enlarging their understanding of the fundamentals of CG and are interested in examining different methods applied to managing a chaotic world observed through coarse-grained lenses.

The filtering approach is a simple deterministic way to formalize analytically coarse-grained representations of a given turbulent flow. By their own nature, turbulence and coarse graining (CG) are multiscaled, and in this chapter, we discuss the specific question of the relations between turbulence, coarse graining, and filtering in a unified operational form, with particular interest to multiscale properties and aspects. Reynolds averaged Navier–Stokes (RANS) averaging, explicit convolutional large eddy simulation (LES) filtering formulations (Leonard, 1975), implicit LES and scale resolving simulations (SRS) approaches (Grinstein et al., 2010; Grinstein, 2016; Pereira et al., 2021), functional and structural LES modeling procedures (Sagaut, 2006) and hybrid RANS/LES methods (Fr¨ohlich and von Terzi, 2008), are revisited and discussed from the point of view of a multiscale operational filtering approach (OFA) (Germano, 1992) based on the multiscale properties of the generalized central moments (GCM). Some recent results are presented both as regards analysis, modeling, and post-processing of turbulent flows, and finally, some conclusions and some personal recalls are provided.