New power-law scaling for friction factor of extreme Reynolds number pipe flows

We report a novel power-law scaling for the friction factor of incompressible Newtonian fluid flows at extreme Reynolds numbers: f = C-e/Re-2/13. The formula is based on a new phenomenology for coherent structures that dominate the momentum exchange in meso-layer regions and scales with the geometric mean <mml:msqrt>delta delta nu</mml:msqrt>, where delta (nu) is the viscous length scale and delta is the pipe radius. Comparisons with the experimental data from the Princeton Superpipe and the Hi-Reff Facility at the National Metrology Institute of Japan show excellent agreement for a large range of Reynolds numbers. This work, along with the recent empirical evidence, suggests a possible change in the mechanism of turbulent momentum transfer for pipe flows in extreme Reynolds numbers.