Turbulent Flows at Very Large Reynolds Numbers: the Lessons of Investigation

Turbulence was the first and the last love of Mikhail Dmitrievich in science. We deeply regret that we are unable to deliver our work to him and to listen his opinion and comments.
Turbulent flows at very large Reynolds numbers ( $\ln Re >> 1$) are generally considered as happy province of the turbulence realm. According to common opinion, two basic results already obtained there, "the von Kármán-Prandtl universal logarithmic law" and Kolmogorov-Obukhov "law of 2/3 (-5/3)" will enter, basically untouched to the future closed in itself theory of turbulence which our mentor, Andrey Nikolaevich Kolmogorov dreamed about. Both these laws are based on the assumption that the flow in its basic region is viscosity independent.
In our lecture the validity of this assumption leading to the universal logarithmic law is discussed in detail. It is shown that it does not correspond to experiment. The universal logarithmic law is founded to be not quite correct, and an alternative law is proposed for the velocity distribution in the shear flows, as well as for the drag law corresponding to it, which are in an instructive agreement with the experiment. Some possible corrections to the Kolmogorov-Obukhov law are also discussed.