# On the Outer Layer Controversy for a Turbulent Boundary Layer over a Rough Wall

## Abstract

An impressive number of experimental and numerical studies of turbulent flows over rough walls has appeared over the last 20 years. Much useful information has been obtained in terms of the turbulence structure both near the roughness canopy and in the outer flow region. However, the issue of whether or not the outer region of the boundary layer is affected by the nature of the wall has yet to be resolved satisfactorily. While the available data, mostly at sufficiently large values of the Reynolds numbers and δ∕*k* (δ and *k* are the boundary layer thickness and characteristic roughness height, respectively), seem to suggest that 3D and transverse 2D rough surfaces may affect the outer layer differently, this suggestion can only be tested rigorously once the measurement of the wall-normal velocity fluctuation over the transverse 2D roughness is improved. With the benefit of the channel flow DNS data, it is argued that, for this latter surface type, the wall shear stress, as inferred from the form drag or drag balance, has actually been measured reasonably accurately in the past.

## Keywords

Wall Shear Stress Reynolds Stress Outer Region Roughness Element Reynolds Shear Stress## Notes

### Acknowledgements

RAA is most grateful to P-A. Krogstad, S. Leonardi and P. Burattini for useful discussions on several issues addressed on in this paper. The past support from the ARC and the collaboration with P. Orlandi, R. Smalley and H. Shafi are warmly acknowledged.

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