Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-18T22:28:34.483Z Has data issue: false hasContentIssue false

Self-preserving flow inside a turbulent boundary layer

Published online by Cambridge University Press:  28 March 2006

A. A. Townsend
Affiliation:
Emmanuel College, Cambridge

Abstract

If a thick, turbulent boundary layer is disturbed near the rigid boundary, the flow changes are confined initially to a thin layer adjacent to the boundary. Elliott (1958) and Panofsky & Townsend (1964) have attempted to calculate the flow disturbance caused by an abrupt change in surface roughness by assuming special velocity distributions which are consistent with a logarithmic velocity variation near the boundary. Inspection of their distributions shows that the deviations from the upstream distribution are self-preserving in form, and it is shown that self-preserving development is dynamically possible if log l0/z0 (l0 being depth of modified flow, z0 roughness length) is fairly large and if l0 is small compared with the total thickness of the layer. Other kinds of surface disturbance may lead to self-preserving changes of the original flow and the theory is developed also for flow downstream of a line roughness, for the temperature distribution downstream of a boundary separating an upstream region of uniform roughness and heat-flux from a region of different or possibly varying roughness and heat-flux, and for the return of a complete boundary layer to self-preserving development after a disturbance. The requirement that the distributions of velocity and temperature should conform to the logarithmic, equilibrium forms near the surface makes the predictions of surface stress and surface flux nearly independent of the exact nature of the turbulent transfer process, and the profiles of velocity and temperature are determined within narrow limits by the surface fluxes. To provide explicit profiles, the mixing-length transfer relation is used. Its validity for the self-preserving flows is discussed in an appendix.

Type
Research Article
Copyright
© 1965 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1957 J. Fluid Mech. 3, 67.
Cermak, J. E. 1963 J. Fluid Mech. 15, 49.
Elliott, W. P. 1958 Trans. Amer. Geophys. Union, 39, 1048.
Ellison, T. H. 1959 Sci. Progr. 47, 495.
Keffer, J. F. 1965 J. Fluid Mech. 22, 135.
Panofsky, H. A. & Townsend, A. A., 1964 Quart. J. Roy. Met. Soc. 90, 147.
Reynolds, A. J. 1963 J. Fluid Mech. 13, 333.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1961 J. Fluid Mech. 11, 97.