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 mesolayer, ${\delta }_m^{+}\sim {\text{Re}}_{\tau }^{1/2}$, and satisfying Kolmogorov's inertial similarity scaling for their turnover velocities. This yields an asymptotic power-law formula for the skin friction, $C_f\sim {\text{Re}}_x^{-2/15}$, or, equivalently, $C_f\sim {\text{Re}}_{\delta }^{-2/13}$. We also derive a 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 semiempirical formulas. For moderately large Re number flows, we argue that the intermediate asymptotic Blasius scaling, $C_f\sim {\text{Re}}_{\delta }^{-1/4}$, or, equivalently, $C_f\sim {\text{Re}}_x^{-1/5}$, is more appropriate. The asymptotic model relies on an asymptotic analysis of the bulk normalized axial mean-momentum equation, and it 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.

Close

PrevNext

View figure in article

• Turbulence
• Turbulent boundary layers