Page "Turbulence" Paragraph 69

Since the experimental values obtained for the second order structure function only deviate slightly from the 2 / 3 value predicted by Kolmogorov theory, the value for p is very near to 5 / 3 ( differences are about 2 %).

Thus the " Kolmogorov-5 / 3 spectrum " is generally observed in turbulence.

However, for high order structure functions the difference with the Kolmogorov scaling is significant, and the breakdown of the statistical self-similarity is clear.

This behavior, and the lack of universality of the constants, are related with the phenomenon of intermittency in turbulence.

This is an important area of research in this field, and a major goal of the modern theory of turbulence is to understand what is really universal in the inertial range.