On the turbulent friction and the near wall structure of pipe flows

Modeling frictional energy losses in turbulent fluid flow often relies on the logarithmic or power-law velocity profiles as definitive representations; however, both approaches have limitations. The power-law model fails at high Reynolds numbers (beyond the Blasius range), while the logarithmic model suffers from uncertainties in its constants, leaving critical questions unresolved. This work analyzes the asymptotic structure of near-wall turbulent flow using scale analysis equations, revealing that the mesolayer is an intrinsic component of the near-wall turbulent regime. By incorporating near-wall dissipative scales, a new formulation is proposed that combines the moderate Reynolds number power-law (Blasius equation) with the high Reynolds number expression. The resulting friction equation demonstrates excellent agreement with experimental data, offering a unified perspective on turbulent flow across a broad range of Reynolds numbers.