ABSTRACT
The physical processes that govern turbulence are far to be all understood, although it attracted a lot of attention in the literature since the nineteenth century. The main impact of A. N. Kolmogorov’s paper lies in a footnote, in which he explains that turbulence can be depicted by a structure of eddies of different scales that interact with each other, the scales being distributed in a continuous range. The chapter considers a homogeneous, isotropic, and stationary turbulence, in the case of smooth solutions of the Navier-Stokes equations (NSE). It defines general homogeneous and isotropic tensors. Kolmogorov’s paper is written from a physical viewpoint, without considering the NSE. The correlation tensors can therefore be specified, yielding the definition of homogeneous and isotropic turbulence. The chapter introduces by this way the Reynolds stress, which plays a central role in the turbulence models.
