Power law and log law velocity profiles in fully developed turbulent pipe flow: equivalent relations at large Reynolds numbers

Abstract

The classical two layers (the inner and outer layers) from open equations of mean turbulent motion, in a fully developed pipe flow, at large Reynolds number in MMX are matched by the application of the Millikan-Kolmogorov hypothesis. In the overlap region, the classical solution of the open functional equation for the velocity profile is the log law region. It is shown here that the open functional equation also possesses another functional solution, the power law velocity profile in the overlap region. The non-unique nature of the solution of the open functional equation predicts both a power law and log law velocity profile. At large Reynolds number the equivalence of the power law and log law is analysed. The comparison of the theory with classical data of Nikuradse and super-pipe data of Zagarola is encouraging.