New friction factor and mean velocity profile for turbulent pipe flow at extreme Reynolds number*

We report on a novel power-law formula for evaluating the friction factor of turbulent incompressible Newtonian fluid flows, f ∼ 1/Re^2/13. The formula is based on a new phenomenology for coherent structures dominating the momentum exchange in mesoregions that are set by the geometric mean of the viscous and outer length scales that have recently been shown to provide the missing link between the flow's viscous and inertial regions.
  The new formula implies a new asymptotic mean velocity profile  of the form u⁺ ∼ A(y⁺-c)^1/12 for the leading order. Comparison with the Princeton superpipe data shows excellent agreement.