Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T18:08:32.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Rough-wall boundary layers: mean flow universality

Published online by Cambridge University Press:  07 August 2007

IAN P. CASTRO
IAN P. CASTRO*
Affiliation:
School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Mean flow profiles, skin friction, and integral parameters for boundary layers developing naturally over a wide variety of fully aerodynamically rough surfaces are presented and discussed. The momentum thickness Reynolds number Reθ extends to values in excess of 47000 and, unlike previous work, a very wide range of the ratio of roughness element height to boundary-layer depth is covered (0.03 < h/δ > 0.5). Comparisons are made with some classical formulations based on the assumption of a universal two-parameter form for the mean velocity profile, and also with other recent measurements. It is shown that appropriately re-written versions of the former can be used to collapse all the data, irrespective of the nature of the roughness, unless the surface is very rough, meaning that the typical roughness element height exceeds some 50% of the boundary-layer momentum thickness, corresponding to about .

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 469 - 485
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Acharya, M., Bornstein, J. & Escudier, M. P. 1986 Turbulent boundary layers on rough surfaces. Exps. Fluids 4, 33–47.CrossRefGoogle Scholar
Antonia, R. A. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. J. Fluid Mech. 48, 721–761.Google Scholar
Bergstrom, D. J., Akinlade, O. G. & Tachie, M. F. 2005 Skin friction correlation for smooth and rough wall turbulent boundary layers. Trans. ASMEI: J. Fluids Engng 127, 1146–1153.Google Scholar
Cheng, H. & Castro, I. P. 2002 Near-wall flow over urban-type roughness. Boundary Layer Met. 104, 229–259.CrossRefGoogle Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.CrossRefGoogle Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.CrossRefGoogle Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. USAF Rep. R-403-PR.Google Scholar
Coles, D. E. 1987 Coherent structures in turbulent boundary layers. In Perspectives in Turbulence Studies (ed. Meier, H. U. & Bradshaw, P.), pp. 93–114. Springer.Google Scholar
Flack, K., Schultz, M. S. & Connelly, J. S. 2007 Examination of a critical roughness height for outer layer similarity. Phys. Fluids. (in press).Google Scholar
Granville, P. S. 1987 Three indirect methods for the drag characterisation of arbitrarily rough surfaces on flat plates. J. Ship Res. 31, 70–77.Google Scholar
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Arch. Mar. Engrs 62, 333–351.Google Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 15–25.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Krogstad, P.-A., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.Google Scholar
Lewcowicz, A. K. 1982 An improved universal wake function for turbulent boundary layers and some of its consequences. Z. Flugwiss. Weltraumforschung 6, 261–266.Google Scholar
Mills, A. F. & Hang, X. 1983 On the skin friction coefficient for a fully rough plate. Trans. ASMEI: J. Fluids Engng 105, 364–365.Google Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. M. & Hites, M. H. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 1–4.CrossRefGoogle Scholar
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth and rough wall turbulent boundary layers. J. Fluid Mech. 177, 437–466.CrossRefGoogle Scholar
Ranga Raju, K. G. Loeser, J. & Plate, E. J. 1976 Velocity profiles and fence drag for a turbulent boundary layer along smooth and rough plates. J. Fluid Mech. 76, 383–399.Google Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Reynolds, R. T., Hayden, P., Castro, I. P. & Robins, A. G. 2007 Spanwise variations in nominally two-dimensional rough-wall boundary layers. Exps. Fluids (in press).CrossRefGoogle Scholar
Rotta, J. C. 1962 The calculation of the turbulent boundary layer. Prog. Aeronaut. Sci. 2, 1–219.CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary Layer Theory, 6th edn. McGraw–Hill.Google Scholar
Snyder, W. H. & Castro, I. P. 2002 The critical Reynolds number for rough-wall boundary layers. J. Wind Engng Indust. Aerodyn. 90, 41–54.CrossRefGoogle Scholar
Tani, I. 1987 Turbulent boundary layer development over rough surfaces. Perspectives in Turbulence Studies(ed. Meier, H. U. & Bradshaw, P.), pp. 223–249. Springer.CrossRefGoogle Scholar
Tutu, N. & Chevray, R. 1975 Cross-wire anemometry in high-intensity turbulence. J. Fluid Mech. 71, 785–800.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar