Boundary-Layer Meteorology

, Volume 116, Issue 3, pp 445–459 | Cite as

New Approaches in Two-equation Turbulence Modelling for Atmospheric Applications



The turbulence closure in atmospheric boundary-layer modelling utilizing Reynolds Averaged Navier–Stokes (RANS) equations at mesoscale as well as at local scale is lacking today a common approach. The standard kɛ model, although it has been successful for local scale problems especially in neutral conditions, is deficient for mesoscale flows without modifications. The kɛ model is re-examined and a new general approach in developing two-equation turbulence models is proposed with the aim of improving their reliability and consequently their range of applicability. This exercise has led to the replacement of the ɛ-transport equation by the transport equation for the turbulence inverse length scale (wavenumber). The present version of the model is restricted to neutrally stratified flows but applicable to both local scale and mesoscale flows. The model capabilities are demonstrated by application to a series of one-dimensional planetary boundary-layer problems and a two-dimensional flow over a square obstacle. For those applications, the present model gave considerably better results than the standard kɛ model.


CFD modelling Eddy viscosity Local scale Mesoscale Turbulence closure Turbulent length scale 


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  1. Andren, A., Moeng, C. H. 1993‘Single Point Closures in a Neutrally Stratified Boundary Layer’J. Atmos. Sci5033663379CrossRefGoogle Scholar
  2. Apsley, D. D., Castro, I. P. 1997‘A Limited-length Scale K–ɛ Model for the Neutral and Stably-Stratified Atmospheric Boundary Layer’Boundary-Layer Meteorol837598CrossRefGoogle Scholar
  3. Bartzis, J. G. 1989‘Turbulent Diffusion Modeling for Wind Flow and Dispersion Analysis’Atmos. Environ2319631969CrossRefGoogle Scholar
  4. Bartzis, J. G. 1991a‘ADREA-I: A Three-dimensional Transport Code for Complex Terrain and Other Applications’Nuclear Technol94135148Google Scholar
  5. Bartzis, J. G.: 1991b, ADREA-HF: A Three-Dimensional Finite Volume Code for Vapor Cloud Dispersion in Complex Terrain, JRC-ISPRA Report, EUR 13580, Italy.Google Scholar
  6. Castro, I. P. 1979‘Relaxing Wakes Behind Surface-mounted Obstacles in Rough Wall Boundary Layers’J. Fluid Mech93631659Google Scholar
  7. Coleman, G. N. 1999‘Similarity Statistics from a Direct Numerical Simulation of the Neutrally Stratified Planetary Boundary Layer’J. Atmos. Sci.56891900CrossRefGoogle Scholar
  8. Coleman, G. N., Ferziger, J. H., Spalart, P. R. 1990‘A Numerical Study of the Turbulent Eckman Layer’J. Fluid Mech213313348Google Scholar
  9. Detering, H. W., Etling, D. 1985‘Application of the E–ɛTurbulence Model to the Atmospheric Boundary Layer’Boundary-Layer Meteorol33113133CrossRefGoogle Scholar
  10. Duynkereke, P. G. 1988‘Application of the E–ɛ Turbulence Model to the Atmospheric Boundary Layer’J. Atmos. Sci45865880CrossRefGoogle Scholar
  11. Garratt, J. R. 1994The Atmospheric Boundary LayerCambridge University PressU.K.316Google Scholar
  12. Kalnay, E. 2003Atmospheric Modelling, Data Assimilation and PredictabilityCambridge University PressU.K141Google Scholar
  13. Kolmogorou, A. N. 1942‘The Equations of Turbulent Motion in an Incompressible Fluid’, Izvestiya Academy of SciencesUSSR; Physics65658Google Scholar
  14. Launder, B. E., Reece, G. J., Rodi, W. 1975‘Progress in the Development of a Reynolds-Stress Turbulence Closure’J. Fluid Mech68313348Google Scholar
  15. McBean G. A. (ed): 1979, The Planetary Boundary Layer, World Meteorological Organization, Tech. Note No 165, 201 pp.Google Scholar
  16. Mellor, G. L., Herring, J. H. 1973‘A Survey of the Mean Turbulent Closure Models’AIAA J11590599Google Scholar
  17. Mellor, G. L., Yamada, T. 1974‘A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers’J. Atmos. Sci3117911806CrossRefGoogle Scholar
  18. Rotta, J. C. 1951‘Statistische Theorie Nichthomogener Turbulenz’Zeitschrift fur Physik129547572CrossRefGoogle Scholar
  19. Troen, I., Mahrt, L. 1986‘A Simple-model of the Atmospheric Boundary-Layer-Sensitivity to Surface Evaporation’Boundary-Layer Meteorol37129148CrossRefGoogle Scholar
  20. Ulden, A. P., Wieringa, J. 1996‘Atmospheric Boundary Layer Research at Cabauw’Boundary-Layer Meteorol783969CrossRefGoogle Scholar
  21. Venetsanos, A. G., Bartzis, J. G., Andronopoulos, S. 2004‘One Equation Turbulence Modeling for Atmospheric and Engineering Applications’Boundary-Layer Meteorol113321346Google Scholar
  22. Walmsley, J. L. 1992‘Proposal for New PBL Resistance Laws for Neutrally Stratified Flow’Boundary-Layer Meteorol60271306CrossRefGoogle Scholar
  23. Weng, W., Taylor, P. A. 2003‘On Modelling the One-Dimensional Atmospheric Boundary Layer’Boundary-Layer Meteorol107371400CrossRefGoogle Scholar
  24. Xu, D., Taylor, P. A. 1997‘An E–ɛ–l Turbulence Closure Scheme for Planetary Boundary layer Models: The Neutrally Stratified Case’Boundary-Layer Meteorol84247266CrossRefGoogle Scholar
  25. Yamada, T. 1983‘Simulation of Nocturnal Drainage Flows by a q2ℓ Turbulence Closure Model’J. Atmos. Sci4091106CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Energy and Resources Management EngineeringUniversity of WesternMacedoniaGreece

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