  One of the key observations in the Princeton Superpipe was the late start of
the logarithmic mean velocity overlap layer at a wall distance of the order of
$10^3$ inner units. Between $y^+\approx 150$, the start of the overlap layer in
zero pressure gradient turbulent boundary layers, and $y^+\approx 10^3$, the
Superpipe profile is modeled equally well by a power law or a log-law with a
larger slope than in the overlap layer. In this paper it is shown that the mean
velocity profile in turbulent plane channel flow exhibits analogous
characteristics, namely a sudden decrease of logarithmic slope (increase of
$\kappa$) at a $y^+_{\mathrm{break}}\approx 600$, which marks the start of the
actual overlap layer. This demonstration results from the first construction of
the complete inner and outer asymptotic expansions up to order
$\mathcal{O}(\mathrm{Re}_\tau)^{-1}$ from mean velocity profiles of direct
numerical simulations (DNS) at moderate Reynolds numbers. A preliminary
analysis of a Couette flow DNS, on the other hand, yields an increase of
logarithmic slope (decrease of $\kappa$) at a $y^+_{\mathrm{break}}\approx
400$. The correlation between the sign of the slope change and the flow
symmetry motivates the hypothesis that the breakpoint between the possibly
universal short inner logarithmic region and the actual overlap log-law
corresponds to the penetration depth of large-scale turbulent structures
originating from the opposite wall.
