Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 505–511 | Cite as

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications

  • S. S. ZilitinkevichEmail author
  • I. Esau
  • N. Kleeorin
  • I. Rogachevskii
  • R. D. Kouznetsov
Open Access
Research Note


We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri =  0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.


Flux Richardson number Stationary and homogeneous regime Strong static stability Turbulence closure Turbulent dissipation length scale Turbulent kinetic energy Velocity gradient 



This work has been supported by the EC FP7 projects ERC PBL-PMES (No. 227915) and MEGAPOLI (No. 212520); and the Norwegian Research Council project 191516/V30 Planetary Boundary Layer Feedback in the Earth’s Climate System.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • S. S. Zilitinkevich
    • 1
    • 2
    • 3
    • 4
    Email author
  • I. Esau
    • 2
    • 5
  • N. Kleeorin
    • 6
  • I. Rogachevskii
    • 6
  • R. D. Kouznetsov
    • 1
    • 3
  1. 1.Finnish Meteorological InstituteHelsinkiFinland
  2. 2.G.C. Rieber Climate InstituteNansen Environmental and Remote Sensing CentreBergenNorway
  3. 3.A.M. Obukhov Institute of Atmospheric PhysicsMoscowRussia
  4. 4.Department of PhysicsUniversity of HelsinkiHelsinkiFinland
  5. 5.Bjerknes Centre for Climate ResearchBergenNorway
  6. 6.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael

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