Subgrid-Scale Modeling

Abstract

In Chapters 3 and 4, we used the ensemble-mean procedure and divided a flow quantity into the large-scale part (mean field) and the fluctuation around it. A prominent feature of the resulting mean field is that its geometrical properties are dependent strongly on boundaries. For instance, the mean flow is one-dimensional in a flow between two parallel plates (channel turbulence) and two-dimensional in a square duct, whereas it is three-dimensional in a flow past a cubic body. In the first two examples, only the highly symmetric components of turbulent motion are retained as the mean field, and all the other components need to be modeled. The resulting system of equations for the mean field is simple, but the burden of the modeling of fluctuation effects becomes heavy, as is seen in Chapter 4. The energy-containing eddies possessing most of the energy of fluctuation, which were referred to in Sec. 3.2.2, are directly linked with the mean flow through the turbulent-energy production process represented by P _K [Eq. (2.112)]. This fact indicates that it is difficult to construct a universal ensemble-mean turbulence model applicable to various types of flows.