ABSTRACT

Early investigators defi ned turbulence as: “an irregular motion which in general makes its appearance in fl uids, gaseous or liquid, when they fl ow past solid surfaces or even when neighboring streams of the same fl uid fl ow past or over one another.” Taylor and Von Karman initiated the

application of statistical theories to describe these irregular motions. A collection of their works is compiled in Friedlander and Topper (1961). Hinze (1975) gave a more precise defi nition as: “Turbulent fl uid motion is an irregular condition of fl ow in which the various quantities show random variation with time and space coordinates, so that statistically distinct average values can be discerned.” An addition to these defi nitions attributed to Bradshaw (Wilcox, 2006) is that “turbulence has a wide range of scales.” Bradshaw (1972) also noted: “Th e problem faced by an engineer, then, is to supply information missing from the time-averaged equations (Reynolds equations) by formulating a model to describe some or all of the six independent Reynolds stresses.” Evaluating all of the Reynolds stresses is not possible, but some partial solutions do exist which are useful for analyzing transport phenomena.