Outer-layer universality of the mean velocity profile in turbulent wall-bounded flows

We derive optimal objective criteria to discern universality of the outer-layer mean velocity profile in wall-bounded flows, which yield a novel set of outer velocity and length scales. The new scaling generalizes the Rotta-Clauser scaling and includes the Zagarola-Smits scaling as a special case for internal flows and supports the friction velocity as the most plausible velocity scale in the asymptotic high-Reynolds-number regime. Composite logarithmic/parabolic formulations are proposed for the mean velocity profile using the classical wall scaling and the new scaling, which yield accurate approximations for boundary layers, pipes and channels.