Since the dynamic equations for turbulent fluids generally show an unstable behaviour, it is practical to use statistical measures of the velocity field rather than trying to make exact predictions.

Most theories for turbulence are based on
Kolmogorov's definitions of
"homogeneous" and "homogeneous isotropic" turbulence
[10]. These definitions are purely statistical, and
basically impossible to test for an experiment, but Kolmogorov argues that the
conditions typically are fulfilled in a small region far from the border of
the system ("small" and "far" as compared to the length scale at which energy
is pumped into the system). Assuming that a fluid system is homogeneous
isotropic turbulent and
that the average behaviour only depends on the average energy dissipation in
the system, it is possible to derive a simple relation between the average
energy dissipation, , velocity differences between particles
separated some distance, , and that distance, *R*.

sparre@cats.nbi.dk