  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.
