Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 513–517 | Cite as

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 2: Observations and Models

  • Rostislav D. KouznetsovEmail author
  • Sergej S. Zilitinkevich
Open Access
Research Note


Observations of the dependence of the dimensionless wind speed gradient \({\phi_m}\) as a function of the Monin–Obukhov stability parameter z/L o under strong stability diverge from results of large-eddy simulation (LES) modelling. A kinetic energy budget analysis indicates that it is likely caused by violations of the assumptions of stationarity and/or homogeneity of turbulence in the field experiments rather than in imperfections of the LES. This confirms the validity of the widely used linear approximation for \({\phi_m}\) not only at weak to moderate stability, but also under strong stability. The new interpretation of the linear approximation of \({\phi_m}\) is given in terms of turbulent scales, which gives hope for its applicability to the free atmosphere as well.


Flux-profile relationships Stable atmospheric boundary layer Turbulent length scale 



We would like to thank Prof. M.A. Kallistratova for helpful discussions, and are grateful to Dr. I. Esau from Nansen Environmental and Research Center for providing the LES database. The SHEBA data were provided by NCAR/EOL under sponsorship of the National Science Foundation ( This work has been supported by the EC FP7 project ERC PBL-PMES (No. 227915) and by Russian Foundation for Basic Research (Grants 08-05-00671 and 10-05-00802).

Open Access

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  1. Basu S, Porté-Agel F (2006) Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: a scale-dependent dynamic modeling approach. J Atmos Sci 63: 2074–2091CrossRefGoogle Scholar
  2. Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189CrossRefGoogle Scholar
  3. Cheng Y, Brutsaert W (2005) Flux-profile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-layer Meteorol 114: 519–538CrossRefGoogle Scholar
  4. Dyer AJ (1974) A review of flux-profile relationships. Boundary-layer Meteorol 7: 363–372CrossRefGoogle Scholar
  5. Esau IN, Zilitinkevich SS (2006) Universal dependences between turbulent and mean flow parameters in stably and neutrally stratified planetary boundary layers. Nonlinear Proc Geophys 13: 135–144CrossRefGoogle Scholar
  6. Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2007) SHEBA flux-profile relationships in the stable atmospheric boundary layer. Boundary-layer Meteorol 124: 315–333CrossRefGoogle Scholar
  7. Hicks BB (1976) Wind profile relationships from the ‘Wangara’ experiment. Q J Roy Meteorol Soc 102: 535–551Google Scholar
  8. Högström U (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary-layer Meteorol 42: 55–78CrossRefGoogle Scholar
  9. McVehil GE (1964) Wind and temperature profiles near the ground in stable stratification. Q J Roy Meteorol Soc 90: 136–146CrossRefGoogle Scholar
  10. Yagüe C, Viana S, Maqueda G, Redondo JM (2006) Influence of stability on the flux-profile relationships for wind speed, Φm, and temperature, Φh, for the stable atmospheric boundary layer. Nonlinear Proc Geophys 13: 185–203CrossRefGoogle Scholar
  11. Zilitinkevich SS, Esau IN (2007) Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer. Boundary-layer Meteorol 125: 193–205CrossRefGoogle Scholar
  12. Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I (2007) Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes. Boundary-layer Meteorol 125: 167–191CrossRefGoogle Scholar
  13. Zilitinkevich SS, Esau I, Kleeorin N, Rogachevskii I, Kouznetsov RD (2010) On the velocity gradient in the stably stratified sheared flows. Part 1: asymptotic analysis and applications. Boundary Layer Meteorol. doi: 10.1007/s10546-010-9488-x

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© The Author(s) 2010

Authors and Affiliations

  • Rostislav D. Kouznetsov
    • 1
    • 2
    Email author
  • Sergej S. Zilitinkevich
    • 1
    • 2
    • 3
    • 4
  1. 1.Finnish Meteorological InstituteHelsinkiFinland
  2. 2.Obukhov Institute of Atmospheric PhysicsMoscowRussia
  3. 3.Division of Atmospheric SciencesUniversity of HelsinkiHelsinkiFinland
  4. 4.Nansen Environmental and Remote Sensing Centre/Bjerknes Centre for Climate ResearchUniversity of BergenBergenNorway

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