On Persen theory of two dimensional turbulent boundary layer

The paper is devoted to the examination of Persen's theory of two dimensional turbulent boundary layers over a smooth flat plate in the light of recent measurements by Österlund. In Persen's approach, the zero-pressure gradient turbulent boundary layer may be divided into two regions only, e.g., I) the inner region, wherein an universally valid structure prevails and modified Spalding's formula is applicable and II) the outer region, which can be described within a similarity framework by a wake law due to Persen. It is shown that the establishment of the theory depends on an experimentally supported relation between the non-dimensional velocity at the end point of the boundary layer and the corresponding non-dimensional distance from the wall. The solution to the problem is achieved by another relation between this velocity and the momentum thickness Reynolds number. The coefficients of skin-friction and velocity profiles, as obtained here for a range of high Reynolds numbers, are found to be in good agreement with Österlund's data. Finally, the results are discussed in the light of the applicability of Österlund's experimental data to the verification of Persen's turbulent boundary layer theory.