Boundary-Layer Meteorology

, Volume 104, Issue 3, pp 371–379 | Cite as

On Integral Measures Of The Neutral Barotropic Planetary Boundary Layer

  • S. S. Zilitinkevich
  • I. N. Esau


Two types of neutral planetary boundary layer (PBL) are distinguished:truly neutral – developed against a neutrally stratified free flow, and conventionally neutral – developed against a background stable stratification. Atmospheric PBLs treated asneutral are almost always conventionally neutral. Theoretical reasoning and results from large-eddy simulation (LES) show that A and B coefficients of the Rossby-number similarity theory are not constants. The same is true for thecoefficient Ch in the Rossby–Montgomery formula for the neutral boundary-layer depth h = Chu*/|f|, where u* is the friction velocity. Contrary to classical ideas, A, B and Ch depend on the ratio μN≡ N/|f| of the free-flow Brunt–V*auml;isäl ä frequency N to the absolute value of the Coriolis parameter |f|. This new development can explain why atmospheric and LES estimates of A, B and Ch appear inconsistent. It results from neglecting the fact that atmospheric data for μN ∼ 102 were compared with LES data for μN = 0, violating an obvious requirement of similarity with respect to μN.

Boundary-layer depth Free-flow stability Neutral boundary layer Resistance law 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andren, A., Brown, A. R., Graf, J., Mason, P. J., Moeng, C.-H., Nieuwstadt, F. T. N., and Schumann, U.: 1994, 'Large-Eddy Simulation of a Neutrally Stratified Layer: A Comparison of Four Computer Codes', Quart. J. Roy. Meteorol. Soc. 120, 1457–1484.Google Scholar
  2. Blackadar, A. K.: 1962, 'The Vertical Distribution of Wind and Turbulent Exchange in a Neutral Atmosphere', J. Geophys. Res. 67, 3095–3102.Google Scholar
  3. Blackadar, A. K.: 1965, A Single-Layer Theory of the Vertical Distribution of Wind in a Baroclinic Neutral Atmospheric Boundary Layer, Final Report AFCRL 65-531, Department of Meteorology, Pennsylvania State University, 22 pp.Google Scholar
  4. Caldwell, D. R., van Atta, C. W., and Heland, K. H.: 1972, 'A Laboratory Study of the Turbulent Ekman Layer', Geophys. Fluid Dyn. 3, 125–160.Google Scholar
  5. Coleman, G. N.: 1999, 'Similarity Statistics from a Direct Numerical Simulation of the Neutrally Stratified Planetary Boundary Layer', J. Atmos. Sci. 56, 891–900.Google Scholar
  6. Esau, I. N.: 2001, 'Large-Eddy Simulation: Theory, Models and Experiments for the Atmospheric Boundary Layer', Introductory Essay, Department of Earth Sciences, Meteorology (MIUU), Uppsala University, 61 pp. Available at MIUU: Villavägen 16, SE-752 36, Uppsala, Sweden.Google Scholar
  7. Grant, A. L. M.: 1986, 'Observations of Boundary Layer Structure Made during the 1981 KONTUR Experiment', Quart. J. Roy. Meteorol. Soc. 112, 825–841.Google Scholar
  8. Hess, G. D. and Garratt, J. R.: 2002a, 'Evaluating Models of the Neutral, Barotropic Planetary Boundary Layer Using Integral Measures: Part I. Overview', Boundary-Layer Meteorol. 104, 333–358.Google Scholar
  9. Hess, G. D. and Garratt, J. R.: 2002b, 'Evaluating Models of the Neutral, Barotropic Planetary Boundary Layer Using Integral Measures: Part II. Modelling Observed Conditions', Boundary-Layer Meteorol. 104, 359–369.Google Scholar
  10. Kazanski, A. B. and Monin, A. S.: 1961, 'On the Dynamic Interaction between the Atmosphere and Earth's Surface', Izv. ANSSSR, Geophys. Ser. No. 5, 514-515.Google Scholar
  11. Lettau, H. H.: 1962, 'Theoretical Wind Spirals in the Boundary Layer of a Barotropic Atmosphere', Beitr. Phys. Atmos. 35, 195–212.Google Scholar
  12. Lin, C.-L., Moeng, C.-H., Sullivan, P. P., and McWilliams, J. C.: 1997, 'The Effect of Surface Roughness on Flow Structures in a Neutrally Stratified Planetary Boundary Layer Flow', Phys. Fluids 9, 3235–3249.Google Scholar
  13. Mason, P. J. and Thomson, D. J.: 1987, 'Large-Eddy Simulations of the Neutral-Static-Stability Planetary Boundary Layer', Quart. J. Roy. Meteorol. Soc. 113, 413–443.Google Scholar
  14. Moeng, C.-H. and Sullivan, P. P.: 1994, 'A Comparison of Shear-and Buoyancy Driven Planetary Boundary Layer Flows', J. Atmos. Sci. 54, 999–1022.Google Scholar
  15. Rossby, C. G. and Montgomery, R. B.: 1935, 'The Layers of Frictional Influence in Wind and Ocean Currents', Pap. Phys. Oceanogr. Meteorol. 3(3), 101 pp.Google Scholar
  16. Sullivan, P. P., McWilliams, J. C., and Moeng, C.-H.: 1994, 'A Subgrid Scale Model for Large Eddy Simulation of Planetary Boundary Layer Flows', Boundary-Layer Meteorol. 71, 247–276.Google Scholar
  17. Taylor, P. A.: 1969, 'On Planetary Boundary Layer Flow under Conditions of Neutral Thermal Stability', J. Atmos. Sci. 26, 427–431.Google Scholar
  18. Zilitinkevich, S. S.: 1967, 'On Dynamic and Thermal Interaction between the Atmosphere and the Ocean', Izvestija AN SSSR, FAO 3, 1069–1077.Google Scholar
  19. Zilitinkevich, S.: 2002, 'Third-Order Transport Due to Internal Waves and Non-Local Turbulence in the Stably Stratified Surface Layer', Quart. J. Roy. Meteorol. Soc. 128, 913–925.Google Scholar
  20. Zilitinkevich, S. S. and Baklanov, A.: 2002, 'Calculation of the Height of Stable Boundary Layers in Practical Applications', Boundary-Layer Meteorol., in press.Google Scholar
  21. Zilitinkevich, S. and Calanca, P.: 2000, 'An Extended Similarity-Theory for the Stably Stratified Atmospheric Surface Layer', Quart. J. Roy. Meteorol. Soc. 126, 1913–1923.Google Scholar
  22. Zilitinkevich, S. S. and Chalikov, D. V.: 1968, 'On the Resistance and Heat/Moisture Transfer Laws in the Interaction between the Atmosphere and the Underlying Surface', Izv. Atmos. Oceanic Phys. 4, 765–772.Google Scholar
  23. Zilitinkevich, S. and Mironov, D. V.: 1996, 'A Multi-Limit Formulation for the Equilibrium Depth of a Stably Stratified Boundary Layer', Boundary-Layer Meteorol. m81, 325–351.Google Scholar
  24. Zilitinkevich, S. S., Baklanov, A., Rost, J., Smedman, A.-S., Lykosov, V., and Calanca, P.: 2002, 'Diagnostic and Prognostic Equations for the Depth of the Stably Stratified Ekman Boundary Layer', Quart. J. Roy. Meteorol. Soc. 128, 25–46.Google Scholar
  25. Zilitinkevich, S., Johansson, P.-E., Mironov, D. V., and Baklanov, A.: 1998, 'A Similarity-Theory Model for Wind Profile and Resistance Law in Stably Stratified Planetary Boundary Layers', J. Wind Engng. Indust. Aerodyn. 74-76, 209–218.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • S. S. Zilitinkevich
    • 1
  • I. N. Esau
    • 1
  1. 1.Department of Earth Sciences, MeteorologyUppsala UniversityUppsalaSweden

Personalised recommendations