Turbulent boundary layers at very large Reynolds numbers

Andrei Nikolaevich Kolmogorov firmly believed that in the absence of a rigorous self-contained theory of turbulent fluids and gases one must use hypotheses obtained by processing experimental data. This paper begins with a discussion of the hypothesis of complete self-similarity used in the proof of the widely known (Reynolds-number independent) von Kármán–Prandtl logarithmic law for the distribution of velocity in a turbulent shear flow. It is shown that this hypothesis has not been confirmed experimentally. Instead, a hypothesis of incomplete self-similarity is proposed which leads to a power-law dependence on the Reynolds number. It is shown that this law agrees well with experiments for the most important classes of turbulent shear flows (for flows in pipes and boundary layers).