Power laws in wall and wake layers of a turbulent boundary layer

TL;DR

This paper explores the power laws in the overlap region of turbulent boundary layers, deriving their relation to log laws and discussing the non-uniqueness of solutions at high Reynolds numbers.

Contribution

It derives power laws in turbulent boundary layers using the Izakson-Millikan-Kolmogorov hypothesis and analyzes their equivalence to log laws at large Reynolds numbers.

Findings

Power laws are obtained for velocity and skin friction.

Power laws are equivalent to log laws at high Reynolds numbers.

Solution of the functional equation is not unique.

Abstract

The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \& skin friction have equivalence with log laws for velocity \& skin friction, for large Reynolds numbers.