Kolmogorov's First Hypothesis

At sufficiently high Reynolds numbers, there is a region of high wave numbers, where the turbulence is statistically in equilibrium and uniquely determined by the parameters and ν . This state of equilibrium is universal.

At this state, the turbulence is statistically homogeneous and locally isotropic.

Consequence of becoming statistically homogeneous:

Between any two points and are same

Equilibrium: The total energy supply is practically equal to total dissipation

Figure 5.2