An Overview

Turbulence is, of course, a phenomenon of immense practical importance and has therefore been extensively studied in the context of its applications, by both engineers and applied scientists. Typically an engineer is concerned with turbulent flow through complicated physical situations, such as heat exchangers or turbines, and needs to predict (for example) the mean velocity of the fluid. As the fundamental problems of the subject are still unsolved, this activity involves the use of various ad hoc assumptions and semi-empirical methods.

In contrast, the physicist wishes to understand the phenomenon, and studies it in the simplest possible situation, where the turbulence is homogeneous and isotropic. Under these circumstances, the objective is to predict the energy spectrum, and the goal here has been provided by a simple dimensional analysis. For sufficiently large values of the Reynolds number, the well-known Kolmogorov spectrum is

E(k)=^2/3k^-5/3,

where is the energy dissipation rate, k is the wavenumber and is a prefactor which does not depend on either of the other two quantities. This result has been amply confirmed by experiment and the calculation of the prefactor - the so-called Kolmogorov constant - is the goal of fundamental theories.