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On Persen theory of two dimensional turbulent boundary layer

Mazumdar H. P., Mandal B. C.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 4

1009-1028

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.

Double-averaged velocity profiles over fixed dune shapes

McLean S. R., Nikora V. I., Coleman S. E.

Acta Geophysica

2008

Vol. 56, no. 3

669-697

Spatially averaged profiles of time averaged velocity, using integrals over thin horizontal slabs (Cartesian double average), are employed in characterizing the flow over fixed dune shapes. For comparison the spatial averaging method of Smith and McLean (1977) that averages along lines at constant distance from the local bed elevation is also investigated. The Cartesian double averaged profiles of the inverse of the velocity shear are nearly constant below the crest elevation, but increase rapidly above the crest level. This results in velocity profiles that increase linearly with distance from the bed below the crest. Above the crest it can be argued that the velocity increases logarithmically, but a power law profile can also be argued. Spatially averaged eddy viscosity profiles are calculated by multiplying the average Reynolds stress by the inverse shear. The resulting profile is more complex than the uniform flow counterpart.