Abstract
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.
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Abbreviations
- DAWA:
-
Department of Agriculture, Western Australia-formerly, West Australian Department of Agriculture and also Agriculture WA
- MTP:
-
Murdoch Turbulence Probe
- XWA:
-
X-Wire Anemometer, a cross-wire, hot-wire anemometer
References
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.
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.
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.
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.
Sutton, O.E.: 1953, Micrometeorology, Kreiger, FL, 33 pp.
Townsend, A.A.: 1956, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 315 pp.
Daily, J.W and Harleman, D.R.F.: 1966, Fluid Dynamics, MA, Addison-Wesley Publishing Company, Reading, MA, 454 pp.
Marshall, J.K.: 1971, Drag measurements in roughness arrays of varying density and distribution, Agric. Meteorol. 8, 269–292.
Bird, R.B., Stewart, W.E. and Lightfoot, E.N.: 2002, Transport Phenomena, John Wiley, 780 pp.
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.)
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.
Tennekes, H. and Lumley, J.L.: 1972, A First Course in Turbulence, MIT Press, Cambridge, MA, 300 pp.
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.
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.
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.
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.
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.
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.
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.
Bagnold, R.A.: 1941, Physics of Blown Sand and Desert Dunes, Chapman and Hall, London 99 pp.
Lyons, T.J. and Scott, W.D.,: 1990, Principles of Air Pollution Meteorology, CRC Press, Boca Raton, FL, 224 pp.
Scott, W.D.: 2001, Maple for Environmental Sciences: A Helping Hand, Section 5.6, Springer-Verlag, 395 pp.
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Findlater, P.A., Scott, W.D., Greenhill, S.E. et al. Estimation of the surface stress from the streamwise pressure gradient: The Kármán Integral Momentum Equation revisited. Environ Fluid Mech 4, 367–383 (2005). https://doi.org/10.1007/s10652-005-6203-4
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DOI: https://doi.org/10.1007/s10652-005-6203-4