Asymptotic scaling laws for the skin friction of zero pressure gradient boundary layers*

We propose a phenomenological description of the asymptotic near-wall momentum exchange mechanism of flat plate zero-pressure gradient turbulent boundary layer flows

at the extreme Reynolds number regime, based on a simple model of attached eddies scaling with the location of the meso-layer, and satisfying Kolmogorov’s inertial similarity scaling for their turnover velocities. This yields a new asymptotic power-law formula for the skin-friction, f ~ Re_x^-2/15 or, equivalently, f ~ Re_δ^-2/15. We also derive a new formula for the asymptotic thickness of the boundary layer. We show that these asymptotic scaling laws are in excellent agreement with experimental data, and are consistent with classical semi-empirical formulas. The asymptotic model is related to a phenomenology previously proposed for pipe and channel flows, which suggests the existence of a universal

transition of the turbulent momentum exchange mechanism of wall-bounded flows in the asymptotically large Re number regime.