Length Scales of the Neutral Wind Profile over Homogeneous Terrain

Alfredo Peña Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Roskilde, and Department of Geography and Geology, University of Copenhagen, Copenhagen, Denmark

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Sven-Erik Gryning Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Roskilde, Denmark

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Jakob Mann Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Roskilde, Denmark

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Charlotte B. Hasager Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Roskilde, Denmark

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Abstract

The wind speed profile for the neutral boundary layer is derived for a number of mixing-length parameterizations, which account for the height of the boundary layer. The wind speed profiles show good agreement with the reanalysis of the Leipzig wind profile (950 m high) and with combined cup–sonic anemometer and lidar measurements (300 m high) performed over flat and homogeneous terrain at Høvsøre, Denmark. In the surface layer, the mixing-length parameterizations agree well with the traditional surface-layer theory, but the wind speed profile is underestimated when the surface-layer scaling is extended to the entire boundary layer, demonstrating the importance of the boundary layer height as a scaling parameter. The turbulence measurements, performed up to 160-m height only at the Høvsøre site, provide the opportunity to derive the spectral-length scales from two spectral models. Good agreement is found between the behaviors of the mixing- and spectral-length scales.

Corresponding author address: Alfredo Peña, Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark. Email: aldi@risoe.dtu.dk

Abstract

The wind speed profile for the neutral boundary layer is derived for a number of mixing-length parameterizations, which account for the height of the boundary layer. The wind speed profiles show good agreement with the reanalysis of the Leipzig wind profile (950 m high) and with combined cup–sonic anemometer and lidar measurements (300 m high) performed over flat and homogeneous terrain at Høvsøre, Denmark. In the surface layer, the mixing-length parameterizations agree well with the traditional surface-layer theory, but the wind speed profile is underestimated when the surface-layer scaling is extended to the entire boundary layer, demonstrating the importance of the boundary layer height as a scaling parameter. The turbulence measurements, performed up to 160-m height only at the Høvsøre site, provide the opportunity to derive the spectral-length scales from two spectral models. Good agreement is found between the behaviors of the mixing- and spectral-length scales.

Corresponding author address: Alfredo Peña, Wind Energy Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark. Email: aldi@risoe.dtu.dk

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  • Andreas, E. L., K. J. Claffey, R. E. Jordan, C. W. Fairall, P. S. Guest, P. O. G. Persson, and A. Grachev, 2006: Evaluations of the von Kármán constant in the atmospheric surface layer. J. Fluid Mech., 559 , 117149.

    • Search Google Scholar
    • Export Citation
  • Bergmann, J. C., 2006: Comments on “The neutral, barotropic planetary boundary layer, capped by a low-level jet inversion”. Bound.-Layer Meteor., 119 , 171179.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., 1962: The vertical distribution of wind and turbulent exchange in a neutral atmosphere. J. Geophys. Res., 67 , 30953102.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., 1965: A single-layer theory of the vertical distribution of wind in a baroclinic neutral atmospheric boundary layer. Flux of Heat and Momentum in the Planetary Boundary Layer of the Atmosphere, The Pennsylvania State University Rep. AFCRL-65-531, 1–22.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., and H. Tennekes, 1968: Asymptotic similarity in neutral barotropic planetary boundary layers. J. Atmos. Sci., 25 , 10151020.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., J. A. Dutton, H. A. Panofsky, and A. Chaplin, 1969: Investigation of the turbulent wind field below 150-m altitude at the eastern test range. NASA Tech. Rep. NASA CR-1410, 92 pp.

    • Search Google Scholar
    • Export Citation
  • Carl, D. M., T. C. Tarbell, and H. A. Panofsky, 1973: Profiles of wind and temperature from towers over homogeneous terrain. J. Atmos. Sci., 30 , 788794.

    • Search Google Scholar
    • Export Citation
  • Clarke, R. H., A. J. Dyer, R. R. Brook, D. G. Reid, and A. J. Troup, 1971: The Wangara experiment: Boundary layer data. CSIRO Tech. Paper 19, 362 pp.

    • Search Google Scholar
    • Export Citation
  • Courtney, M., R. Wagner, and P. Lindelöw, 2008: Testing and comparison of lidars for profile and turbulence measurements in wind energy. Earth Environ. Sci., 1 , 012021. doi:10.1088/1755-1315/1/1/012021.

    • Search Google Scholar
    • Export Citation
  • Derbyshire, S. H., and J. C. R. Hunt, 1993: Structure of turbulence in stably stratified atmospheric boundary layers: Comparison of large-eddy simulations and theoretical models. Waves and Turbulence in Stably Stratified Flows, S. D. Moobs and J. C. King, Eds., Clarendon, 23–59.

    • Search Google Scholar
    • Export Citation
  • Estoque, M. A., 1973: Numerical modeling of the planetary boundary layer. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 217–270.

    • Search Google Scholar
    • Export Citation
  • Gryning, S-E., E. Batchvarova, B. Brümmer, H. Jørgensen, and S. Larsen, 2007: On the extension of the wind profile over homogeneous terrain beyond the surface layer. Bound.-Layer Meteor., 124 , 251268.

    • Search Google Scholar
    • Export Citation
  • Hess, G. D., 2004: The neutral, barotropic planetary boundary layer, capped by a low-level inversion. Bound.-Layer Meteor., 110 , 319355.

    • Search Google Scholar
    • Export Citation
  • Hess, G. D., 2006: Reply to “Comments on ‘The neutral, barotropic planetary boundary layer, capped by a low-level jet inversion’”. Bound.-Layer Meteor., 119 , 181194.

    • Search Google Scholar
    • Export Citation
  • Hess, G. D., and J. R. Garratt, 2002: Evaluating models of the neutral, barotropic planetary boundary layer using integral measures. Part I: Overview. Bound.-Layer Meteor., 104 , 333358.

    • Search Google Scholar
    • Export Citation
  • Högström, U., 1988: Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Bound.-Layer Meteor., 42 , 5578.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A. A. M., 1984: Estimates of diabatic wind speed profiles from near-surface weather observations. Bound.-Layer Meteor., 29 , 225250.

    • Search Google Scholar
    • Export Citation
  • Jørgensen, H. E., T. Mikkelsen, S-E. Gryning, S. Larsen, P. Astrup, and P. E. Sørensen, 2008: Measurements from Høvsøre met mast. Tech. Rep. Risø-R-1592(EN), Risø National Laboratory, 32 pp.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 289 pp.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., J. C. Wyngaard, Y. Izumi, and O. R. Coté, 1972: Spectral characteristics of surface-layer turbulence. Quart. J. Roy. Meteor. Soc., 98 , 563589.

    • Search Google Scholar
    • Export Citation
  • Kazanskii, A. B., and A. S. Monin, 1961: On the dynamical interaction between the atmosphere and the earth’s surface (in Russian). Bull. Acad. Sci. USSR. Ser. Geophys., 5 , 786788.

    • Search Google Scholar
    • Export Citation
  • Kindler, D., A. Oldroyd, A. MacAskill, and D. Finch, 2007: An eight-month test campaign of the QinetiQ ZephIR system: Preliminary results. Meteor. Z., 16 (5) 479489.

    • Search Google Scholar
    • Export Citation
  • Landau, L. D., and E. M. Lifshitz, 1987: Fluid Mechanics. Pergamon Press, 539 pp.

  • Landberg, L., L. Myllerup, O. Rathmann, E. L. Petersen, B. H. Jorgensen, J. Badger, and N. G. Mortensen, 2003: Wind resource estimation: An overview. Wind Energy, 6 , 261271.

    • Search Google Scholar
    • Export Citation
  • Lettau, H., 1950: A re-examination of the Leipzig wind profile considering some relations between wind and turbulence in the frictional layer. Tellus, 2 , 125129.

    • Search Google Scholar
    • Export Citation
  • Lettau, H., 1962: Theoretical wind spirals in the boundary layer of a barotropic atmosphere. Beitr. Phys. Atmos., 35 , 195212.

  • Liu, H., G. Peters, and T. Foken, 2001: New equations for sonic temperature variance and buoyancy heat flux with an omnidirectional sonic anemometer. Bound.-Layer Meteor., 100 , 459468.

    • Search Google Scholar
    • Export Citation
  • Mann, J., 1994: The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech., 273 , 141168.

  • Mann, J., E. Dellwik, F. Bingöl, and O. Rathmann, 2007: Laser measurements of flow over a forest. Earth Environ. Sci., 1 , 012050. doi:10.1088/1755-1307/1/1/012050.

    • Search Google Scholar
    • Export Citation
  • Mann, J., and Coauthors, 2009: Comparison of 3D turbulence measurements using three staring wind lidars and a sonic anemometer. Meteor. Z., 18 , 135140.

    • Search Google Scholar
    • Export Citation
  • Maxey, M. R., 1982: Distortion of turbulence in flows with parallel streamlines. J. Fluid Mech., 124 , 261282.

  • Mildner, P., 1932: Über die Reibung in einer speziellen Luftmasse in den untersten Schichten der Atmosphäre (On the friction inside a particular air mass in the lowest layers of the atmosphere). Beitr. Phys. Atmos., 19 , 151158.

    • Search Google Scholar
    • Export Citation
  • Ohmstede, W. D., and J. F. Appleby, 1964: Numerical solution of the distribution of wind and turbulence in the planetary boundary layer. Meteor. Res. Note 8, DA Task 1-A-0-11001-B-021-08, 43 pp.

    • Search Google Scholar
    • Export Citation
  • Panofsky, H. A., 1973: Tower micrometeorology. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 151–176.

  • Panofsky, H. A., and E. L. Petersen, 1972: Wind profiles and change of terrain roughness at Risø. Quart. J. Roy. Meteor. Soc., 98 , 845854.

    • Search Google Scholar
    • Export Citation
  • Peña, A., and S-E. Gryning, 2008: Charnock’s roughness length model and non-dimensional wind profiles over the sea. Bound.-Layer Meteor., 128 , 191203.

    • Search Google Scholar
    • Export Citation
  • Peña, A., S-E. Gryning, and C. B. Hasager, 2008: Measurements and modelling of the wind speed profile in the marine atmospheric boundary layer. Bound.-Layer Meteor., 129 , 479495.

    • Search Google Scholar
    • Export Citation
  • Peña, A., C. B. Hasager, S-E. Gryning, M. Courtney, I. Antoniou, and T. Mikkelsen, 2009: Offshore wind profiling using light detection and ranging measurements. Wind Energy, 12 , 105124.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1925: Bericht über Untersuchungen zur ausgebildeten Turbulenz (Report on the investigations of developed turbulence). Z. Angew. Math. Mech., 5 , 136139.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1932: Meteorologische Anwendung der Strömungslehre (Meteorological application of fluid mechanics). Beitr. Phys. Atmos., 19 , 188202.

    • Search Google Scholar
    • Export Citation
  • Rossby, C. G., and R. B. Montgomery, 1935: The layers of frictional influence in wind and ocean currents. Pap. Phys. Oceanogr. Meteor., 3 (3) 1101.

    • Search Google Scholar
    • Export Citation
  • Smith, D. A., M. Harris, A. S. Coffey, T. Mikkelsen, H. E. Jørgensen, J. Mann, and R. Danielian, 2006: Wind lidar evaluation at the Danish wind test site in Høvsøre. Wind Energy, 9 , 8793.

    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Tennekes, H., 1973: Similarity laws and scale relations in planetary boundary layers. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 177–216.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C., and O. R. Coté, 1972: Cospectral similarity in the atmospheric surface layer. Quart. J. Roy. Meteor. Soc., 98 , 590603.

    • Search Google Scholar
    • Export Citation
  • Zanoun, E-S., F. Durst, and H. Nagib, 2003: Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows. Phys. Fluids, 15 , 3079. doi:10.1063/1.1608010.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., 1989: Velocity profiles, the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer. Bound.-Layer Meteor., 46 , 367387.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., and I. N. Esau, 2002: On integral measures of the neutral barotropic planetary boundary layer. Bound.-Layer Meteor., 104 , 371379.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., and I. N. Esau, 2005: Resistance and heat-transfer laws for stable and neutral planetary boundary layers: Old theory advanced and re-evaluated. Quart. J. Roy. Meteor. Soc., 131 , 18631892.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S. S., A. Baklanov, J. Rost, A-S. Smedman, V. Lykosov, and P. Calanca, 2002: Diagnostic and prognostic equations for the depth of the stably stratified Ekman boundary layer. Quart. J. Roy. Meteor. Soc., 128 , 2546.

    • Search Google Scholar
    • Export Citation
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