Rough-conduit flows and the existence of fully developed turbulence

It is widely believed that at high Reynolds number (Re) all turbulent flows approach a state of "fully developed turbulence" defined by a unique, Re-independent statistics of the velocity fluctuations. Yet direct measurements of the velocity fluctuations have failed to yield clear-cut empirical evidence of the existence of fully developed turbulence. Here we relate the friction coefficient ($f$) of rough-conduit flows to the statistics of the velocity fluctuations. In light of experimental measurements of $f$, our results yield unequivocal evidence of the existence of fully developed turbulence.Comment: 5 pages, 2 figure

Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory

The classical experiments on turbulent friction in rough pipes were performed by J. Nikuradse in the 1930's. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmog\'orov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler, and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existence of close ties between two milestones of experimental and theoretical turbulence.Comment: Accepted for publication in PRL; 4 pages, 4 figures; revised versio