Rotta skin friction law and Schoenherr formula

Abstract

This paper examines the Rotta skin friction law (1950) and the Schoenherr empirical formula (1932) for flat plate turbulent boundary layers in the light of direct skin friction measurements conducted in the range of the momentum thickness Reynolds number up to Rθ = 2.13 × 105. First, we demonstrate that the skin friction data almost perfectly follow the Rotta skin friction law derived by assuming the existence of the logarithmic overlap region and by using the velocity profile constants determined by Nagib et al (2007 Phil. Trans. R. Soc. A 365 755–70). Next, we clarify the high Reynolds number asymptotic form of the Rotta law and derive the Schoenherr empirical formula from the asymptotic relation. The Schoenherr formula is shown to be a good approximation to the Rotta skin friction law for Rθ greater than 1.1×104. Above all, the present effort yields a new formula for the local skin friction, which is almost identical with the Rotta skin friction law in accuracy, with the relative deviation being less than 0.05% in the range of Cf less than 0.0037.