Fourier Analysis of Homogeneous Turbulence

Abstract

When the turbulence is homogeneous, i.e. statistically invariant under translations, it is extremely useful to work in the Fourier space. In this chapter various Fourier representations of a statistically homogeneous turbulent flow will be presented, as well as the Navier-Stokes equations or the Boussinesq approximation projected in that space. We will discuss utilization of random functions for the study of turbulence, and describe the properties of isotropic turbulence (statistically invariant under rotations). Helical turbulence will be considered, with the helical-wave decomposition of the velocity field. We will look also briefly at axisymmetric turbulence. Finally, we will see how rapid-distorsion theory applies to homogeneous turbulence submitted to a plane strain.