Turbulent Flows

One can arguably assume that the start of turbulence research as we view it within the context of conservation equations and statistical correlations began in the late nineteenth century. The seminal papers of Boussinesq (Mém Acad Sci Inst Fr 23:46–50, 1877) and Reynolds (Philos Trans R Soc Lond A 186:123–164, 1895) dealing with turbulent momentum transfer and statistical averages of turbulent fluctuations still lie at the core of the research being conducted today. Not until the middle of the last century did texts on the subject begin to appear in the form of monographs focused on either homogeneous turbulence (Batchelor, Homogeneous turbulence, 1953) where theoretical analysis was tractable or turbulent shear flows (Townsend, The structure of turbulent shear flows, 1956) where the emphasis shifted to the extensive experimental results that had been gathered up to that point. These early monographs were soon augmented with texts (Hinze, Turbulence, 1959; Lumley, Stochastic tools in turbulence, 1970a; Monin and Yaglom, Statistical fluid mechanics, vols. 1 and 2, 1971) dealing more rigorously with the (statistical) theoretical aspects. The first text directed mainly at introducing students to the subject was Tennekes and Lumley (A first course in turbulence, 1972) and this marked the beginning of an era that continues today where numerical solutions have become as, or sometimes more, important in turbulence research as physical experiments. A recent presentation including modeling and simulation considerations is given in the book by Pope (Turbulent flows, 2000). Although the primary focus in this chapter is on the incompressible flows and Newtonian fluids, there has also been much effort directed toward high-speed flows and compressible turbulence and now, within the last decade, to viscoelastic, polymeric fluids.