A note on von Kármán's constant in low Reynolds number turbulent flows

Abstract

An analysis of existing data on low Reynolds number flows strongly suggests that the conclusion of Simpson (1970) concerning the variation of von Kármás constant κ with Reynolds number is not correct. This implies that Coles’ (1962) assumption of the validity of the logarithmic velocity profile at low Reynolds numbers is correct and, moreover, that the inference drawn by Coles and later authors regarding the presence of viscous effects in the outer layer is valid. The analysis shows that these viscous effects are not present in duct flows, so that they are presumably associated with the presence of a turbulent-irrotational interface; it is argued that the ‘viscous superlayer’ can affect a large part of the outer layer at low Reynolds numbers. The data analysis incidentally shows that the viscous sublayer is more strongly affected by shear-stress gradients or transverse wall curvature than is the rest of the inner layer.