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

We derive objective criteria to discern universality of the outer-layer mean velocity profile in wall-bounded flows, which yield a 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 it supports the friction velocity as the most plausible velocity scale in the asymptotic high-Reynolds-number regime. A composite logarithmic/parabolic formulation is proposed for the outer mean velocity profile, which yields simple and accurate approximations for boundary layers, pipes, and channels.