Power law scaling of the friction factor in pipe flow

We present a study of the friction factor scaling for pipe and duct flows at moderate Reynolds numbers (5000<Re<150 000) in experiments and highly resolved direct numerical simulations.
While the experimental and numerical data are in excellent agreement, we find that for Re<80 000 they do not follow the Karman-Prandtl friction relation. Instead the friction factor precisely
follows the Blasius power law. This power law scaling can also be derived based on
Kolmogorov's first hypothesis (assuming local isotropy) in line with an earlier study. A detailed analysis of the numerical data shows that flows in this Reynolds number regime are indeed locally isotropic and that hence the application of the Kolmogorov theory is justified. Finally, we will show that the deviation of the friction factor from the power law scaling (Re>80 000) occurs when large scale motions (so-called ``superstructures'') arise in the flow and their contribution to the friction factor becomes dominant.