Kolmogorov's Second Hypothesis

At sufficiently high Reynolds numbers, the statistics of the motions of scale l in the range l_e >>l>> have a universal form that is uniquely determined by , independent of .

Length scale l correspond to wave number,

So in the second hypothesis k_e<<k<<k_d,      

Spectrum indicates how the turbulent kinetic energy is distributed among the eddies of different sizes. From the second hypothesis, the spectrum is

The region in which this is valid is called the inertial subrange of universal equilibrium.

In this range of wave numbers, the inertial forces play a dominant role, while the viscous forces become insignificant.

The universal function has to be determined experimentally. To be noted <<1.

Figure 5.3