The importance of higher-order effects in the Barenblatt–Chorin theory of wall-bounded fully developed turbulent shear flows

Barenblatt [J. Fluid Mech. 248, 513 (1993)] proposed a Reynolds number (R)-dependent power law for the mean velocity near the wall in fully developed turbulent shear flows. In an appropriate region, as R→∞, the envelope of the velocity profiles reduces to a logarithmic law with an additive constant that is significantly larger than that of the universal logarithmic law. This discrepancy is removed upon including a higher-order term in the power-law exponent. Using the friction (instead of average) velocity in the definition of R destroys the invariance of the nonvanishing higher-order terms of the power law as R→∞.