Environmental Fluid Mechanics

, Volume 4, Issue 4, pp 367–383 | Cite as

Estimation of the surface stress from the streamwise pressure gradient: The Kármán Integral Momentum Equation revisited

  • P. A. Findlater
  • W. D. Scott
  • S. E. Greenhill
  • J. M. Hopwood


A method is developed to estimate the stress at the surface in a portable wind tunnel for wind erosion studies. The boundary layer height and the pressure gradient are used in a simple expression from the Kármán Integral Momentum Equation. Values of friction velocity u* are within 10% of experimental values obtained through correlation techniques, including measurements of differential pressures with the Murdoch Turbulence Probe MTP and the X-wire, hot-wire anemometer XWA. Wind velocity and stress profiles reveal logarithmic trends and a ‘constant stress layer’ near the surface in the DAWA portable wind tunnel. Realignment of the statistics with the mean wind is essential.

Key words

agriculture cross-wire erosion hot-wire integral Kármán karman momentum Murdoch Turbulence Probe shear stress wind tunnel 



Department of Agriculture, Western Australia-formerly, West Australian Department of Agriculture and also Agriculture WA


Murdoch Turbulence Probe


X-Wire Anemometer, a cross-wire, hot-wire anemometer


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Findlater, P.A., Greenhill, S.E., and W.D. Scott: 2001, Design and testing of a turbulence probe for harsh flows, J. Environ. Fluid Mech., 1, March.Google Scholar
  2. 2.
    Antonia, R.A. and Luxton, R.E.: 1971, The response of the turbulent boundary layer to a step change in surface roughness. Part 1. Smooth-to-rough, J. Fluid Mech. 48, 721–761.Google Scholar
  3. 3.
    Antonia, R.A. and Luxton, R.E.: 1972, The response of the turbulent boundary layer to a step change in surface roughness. Part 2. Rough-to-smooth, J. Fluid Mech. 53, 737–757.Google Scholar
  4. 4.
    von Kármán, Th.: 1921, Über laminare und turbulente Reibung (About laminar and turbulent friction), ZAMM (Zeitschrift für angewandte Mathematik und Mechanik) 1, 233–253. English translation in NACA (National Advisory Committee for Aeronautics, now NASA) Technical Memorandum TM 1092 ; see also Collected Works II, 70–97, London 1956; from Schlichting, Ibid, pp. 159 and 162.Google Scholar
  5. 5.
    Sutton, O.E.: 1953, Micrometeorology, Kreiger, FL, 33 pp.Google Scholar
  6. 6.
    Townsend, A.A.: 1956, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 315 pp.Google Scholar
  7. 7.
    Daily, J.W and Harleman, D.R.F.: 1966, Fluid Dynamics, MA, Addison-Wesley Publishing Company, Reading, MA, 454 pp.Google Scholar
  8. 8.
    Marshall, J.K.: 1971, Drag measurements in roughness arrays of varying density and distribution, Agric. Meteorol. 8, 269–292.Google Scholar
  9. 9.
    Bird, R.B., Stewart, W.E. and Lightfoot, E.N.: 2002, Transport Phenomena, John Wiley, 780 pp.Google Scholar
  10. 10.
    Schlichting, H., and Gersten, K.: 2000, Boundary-Layer Theory, 8th Revised Edition, Springer-Verlag, Berlin, 799 pp. (See also Schlichting, Boundary-Layer Theory, McGraw-Hill, New York.)Google Scholar
  11. 11.
    Carminati, J., Devitt, J.S., and Scott, W.D.: 1995, On the non-uniqueness of solutions in the modelling of steady wind flows, Comput. Fluids 24, 177–188.Google Scholar
  12. 12.
    Tennekes, H. and Lumley, J.L.: 1972, A First Course in Turbulence, MIT Press, Cambridge, MA, 300 pp.Google Scholar
  13. 13.
    Findlater, P.A. Carter, D.J. and Scott, W.D.: 1990, A model to predict the effects of prostrate ground cover on wind erosion, Aust. J. Soil Res. 28, 609–622.Google Scholar
  14. 14.
    Brancatisano, A. and Trinh, D.T.: 1990, Flow Conditions in a Wind Tunnel-Transition Section, Bachelor of Engineering Project Report, Department of Mechanical Engineering, Curtin University of Techology, 139 pp. See also the Report from the Wind Erosion Study Group: 1992, Erosion Wind Tunnel Workshop, Environmental Science Report 92/8, ISBN No. 0-86905-448-1.Google Scholar
  15. 15.
    Raupach, M.R., Thom, A.S. and Edwards, I.: 1980, A wind tunnel study of turbulent flow close to regularly arrayed rough surfaces, Boundary-Layer Meteorol. 18, 373–397.Google Scholar
  16. 16.
    Smith, S.E.: 1994, An Instrument for Measuring Turbulence during Wind Erosion, Ph.D. Thesis and Report 94/3, School of Environmental Science, Murdoch University, Perth, Western Australia.Google Scholar
  17. 17.
    Scott, W.D., Twomey, C., Butcher, L. and Kerr, J.: 1993, The Murdoch Turbulence Probe (19 min VHS Video), Academic Services Unit, Murdoch University, Perth, Western Australia.Google Scholar
  18. 18.
    Findlater, P.A.: 2004, Using a Portable Wind Tunnel as a Tool to Predict Wind Erosivity, Ph.D., School of Environmental Science, Murdoch University, Perth, Western Australia, Australia.Google Scholar
  19. 19.
    Raupach, M.R. and Leys, J.F.: 1990, Aerodynamics of a portable wind erosion tunnel for measuring soil erodibility by wind, Aust. J. Soil Res. 28, 177–191.Google Scholar
  20. 20.
    Bagnold, R.A.: 1941, Physics of Blown Sand and Desert Dunes, Chapman and Hall, London 99 pp.Google Scholar
  21. 21.
    Lyons, T.J. and Scott, W.D.,: 1990, Principles of Air Pollution Meteorology, CRC Press, Boca Raton, FL, 224 pp.Google Scholar
  22. 22.
    Scott, W.D.: 2001, Maple for Environmental Sciences: A Helping Hand, Section 5.6, Springer-Verlag, 395 pp.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • P. A. Findlater
    • 1
  • W. D. Scott
    • 2
  • S. E. Greenhill
    • 2
  • J. M. Hopwood
    • 3
  1. 1.Department of AgricultureWestern AustraliaGeraldton
  2. 2.Murdoch UniversityMurdoch
  3. 3.University of Western AustraliaCrawley

Personalised recommendations