Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T13:26:08.027Z Has data issue: false hasContentIssue false
  • English
  • Français

On the displacement height in the logarithmic velocity profile

Published online by Cambridge University Press:  20 April 2006

P. S. Jackson
P. S. Jackson
Affiliation:
Department of Mechanical Engineering, Auckland University
Get access Rights & Permissions [Opens in a new window]

Abstract

The displacement height appears in the logarithmic velocity profile for rough-wall boundary layers as a reference height for the vertical co-ordinate. It is shown that this height should be regarded as the level at which the mean drag on the surface appears to act. The equations of motion then show that this also coincides with the average displacement thickness for the shear stress.

A simple analytical model, experimental results and dimensional analysis are all used to indicate how the displacement height depends upon the detailed geometry of the roughness elements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 15 - 25
Copyright
© 1981 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

Blihco, R. G. & Partheniades, E. 1971 Turbulence characteristics in free surface flows over smooth and rough boundaries. J. Hyd. Res. 9, 43–69.Google Scholar
Cionco, R. M. 1972 A wind-profile index for canopy flow. Boundary-Layer Met. 3, 225–263.Google Scholar
Counihan, J. 1971 Wind tunnel determination of the roughness length as a function of the fetch and the roughness density of three dimensional elements. Atmos. Environ. 5, 637–642.Google Scholar
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233–255.Google Scholar
Inoue, E. 1963 On the turbulent structure of airflow within crop canopies. J. Met. Soc. Japan 41, 317–326.Google Scholar
Kamphius, J. W. 1974 Determination of sand roughness for fixed beds. J. Hyd. Res. 12, 193–203.Google Scholar
Kondo, J. 1971 Relationship between the roughness coefficient and other aerodynamic parameters. J. Met. Soc. Japan 49, 121–124.Google Scholar
Lee, B. E. & Soliman, B. F. 1977 An investigation of the forces on three-dimensional bluff bodies in rough wall turbulent boundary layers. Trans. A.S.M.E. I, J. Fluids Engng 99, 503–510.Google Scholar
Oke, T. R. 1974 Review of urban climatology, 1968–1973. W.M.O. Tech. Note no. 134.Google Scholar
O'Loughlin, E. M. & Annambhotla, V. S. 1969 Flow phenomena near rough boundaries. J. Hyd. Res. 7, 231–250.Google Scholar
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.Google Scholar
Sayre, W. W. & Albertson, M. L. 1963 Roughness spacing in rigid open channels. Trans. A.S.C.E. 128, 343–427.Google Scholar
Stanhill, G. 1969 A simple instrument for the field measurement of turbulent diffusion flux. J. Appl. Met. 8, 509–513.Google Scholar
Thom, A. S. 1971 Momentum absorption by vegetation. Quart. J. Roy. Met. Soc. 97, 414–428.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.