Scaling of global properties of fluctuating streamwise velocities in pipe flow: Impact of the viscous term

Abstract

We extend the procedure outlined in [Basse, "Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: Characterization of a high Reynolds number transition region," Phys. Fluids Vol. 33, 065127 (2021)] to study global, i.e. radially averaged, scaling of streamwise velocity fluctuations. A viscous term is added to the log-law scaling which leads to the existence of a mathematical abstraction which we call the "global peak". The position and amplitude of this global peak are characterized and compared to the inner and outer peaks. A transition at a friction Reynolds number of order 10000 is identified. Consequences for the global peak scaling, length scales, non-zero asymptotic viscosity, turbulent energy production/dissipation and turbulence intensity scaling are appraised along with the impact of including an additional wake term.