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

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 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.

Automated summary

The study extends a procedure outlined in Basse's work to investigate the global scaling of streamwise velocity fluctuations and identifies a transition at a friction Reynolds number of order 10000. The position and amplitude of the global peak are characterized and the impact of including an additional wake term is analyzed.