Time-mean Turbulent Shear Flows: Classical Modelling — Asymptotic Analysis — New Perspectives

This contribution gives an introduction to the description of timeaveraged single-phase turbulent flows where the largeness of the typical Reynolds numbers at play is their essential characteristic. Hence, the full Navier–Stokes equations form the starting point, and the viewpoint is a most rigorous asymptotic one. Emphasis is placed on the aspects of modelling the unclosed terms in the accordingly Reynolds-averaged equations when governing slender shear flows. Such represent the natural manifestation of turbulence as triggered internally in laminar shear layers by the no-slip condition to be satisfied at rigid walls rather than by free-stream turbulence, neglected here. Given the inherent closure problem associated with the separation and interaction of the variety of spatial/temporal scales involved, this focus allows for a surprisingly deep understanding of turbulent flows resorting to formal asymptotic techniques under the premise of a minimum of reliable assumptions. These are motivated by physical intuition and/or based on classical findings of the statistical theory of locally isotropic turbulence. Intrinsic differences to the analysis of related problems dealing with laminar high-Reynoldsnumber flows are highlighted. Finally, the crucial aspects of numerical simulation of turbulent flows are considered for the staggered levels of filtering, ranging from a most complete resolution to full averaging.