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The flow in a turbulent boundary layer after a change in surface roughness

Published online by Cambridge University Press:  28 March 2006

A. A. Townsend
A. A. Townsend
Affiliation:
Emmanuel College, Cambridge
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Abstract

The changes of surface stress in a deep boundary layer passing from a surface of one roughness to another of different roughness are described fairly accurately by theories that assume self-preserving development of the flow modifications. It has been shown that the dynamical conditions for self-preserving flow can be satisfied if the change in friction velocity is small and if log l0/z0 is large (l0 is the depth of the modified flow and z0 is the roughness length of the surface). In this paper it is shown that, if the change of friction velocity is not small, the dynamical conditions can be satisfied to a good approximation over considerable fetches if log l0/z0 is large. The flow modification is then locally self-preserving, that is, the fields of mean velocity and turbulence are in a moving equilibrium but one which changes very slowly with fetch and depends on the ratio of the initial to the current friction velocity. In the limit of a very large increase in friction velocity, the moving equilibrium is essentially that of a boundary layer developing in a non-turbulent free stream. Equations describing the flow development are derived for all changes of friction velocity, and the form of the velocity changes is discussed. For large increases of friction velocity, the depth of the modified layer is substantially less than would be expected from the theories of Elliott and of Panofsky & Townsend.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 26 , Issue 2 , October 1966 , pp. 255 - 266
Copyright
© 1966 Cambridge University Press

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References

Bradley, E. F. 1965 Ph.D. dissertation, Australian National University.
Elliott, W. P. 1958 Trans. Amer. Geophys. Union 39, 104.
Lettau, H. H. et al. 1962 U.S. Army Electronic Proving Ground Annual Rep., DA 36–039-SC-80282.
Panofsky, H. A. & Townsend, A. A. 1964 Quart. J. Roy. Met. Soc. 90, 14.
Rider, N. E., Philip, J. R. & Bradley, E. F. 1963 Quart. J. Roy. Nat. Soc. 89, 50.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1965a J. Fluid Mech. 22, 77.
Townsend, A. A. 1965b J. Fluid Mech. 22, 79.