Turbulence Modelling

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


The first basic thoughts and experiments on turbulence are due to Reynolds [20] who studied the flow of a fluid through pipes with circular cross-sections. He recognised (by adding dye through a pipette to the fluid) that, basically, two flow regimes exist. In one case, the so-called laminar flow , the dye forms a coherent thin filament; in the second case, known as turbulent flow , the dye filament is torn very quickly after it left the nozzle of the pipette and is spread over the entire cross-section of the pipe; Fig. 6.1.


Turbulent Kinetic Energy Large Eddy Simulation Direct Numerical Simulation Mass Flux Reynolds Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press, Cambridge, 197 p. (1953)Google Scholar
  2. 2.
    Bäuerle, E., Chubarenko, B., Chubarenko, I., Halder, J., Hutter, K. and Wang, Y.: Autumn Physical Limnological Experimental Campaign in the Mainau Island Littoral Zone of Lake Constance (Constance Data Band) 12 October – 19 November 2001. Report of the ‘Sonderforschungsbereich 454 Bodenseelittoral’, 85 p. (2002)Google Scholar
  3. 3.
    Boussinesq, J.: Essay sur la théorie des eaux courantes. Mémoires présenté’s par div. Savants à’ l’ Academie des Sciences de’linstitut de France. Tome 23 (avec supp. in Tome 24), (1877)Google Scholar
  4. 4.
    Frisch, U.: Turbulence, the Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge, 296 p. (1995)Google Scholar
  5. 5.
    Hansalic, K. and Launder, B.E.: A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609–638 (1972)CrossRefGoogle Scholar
  6. 6.
    Hinze, J.O.: Turbulence. McGraw Hill, New York NY, 790 p. (1975)Google Scholar
  7. 7.
    Hutter, K. and Jöhnk, K.: Continuum Methods of Physical Modeling. Springer, Berlin, 635 p. (2004)Google Scholar
  8. 8.
    Jones, W.P. and Launder, B.E.: The prediction of laminarisation with a two-equation model of turbulence. J. Heat Mass Transf. 15, 301–314 (1972)CrossRefGoogle Scholar
  9. 9.
    Launder, B.E. and Spalding, D.B.: The numerical computation of turbulent flow. Comp. Meth. Appl. Mech. Eng. 3, 269–288 (1974)CrossRefGoogle Scholar
  10. 10.
    Lesieur, M.: Turbulence in Fluids. Kluwer, Dordrecht, 411 p. (1990)CrossRefGoogle Scholar
  11. 11.
    Lumley, J.L.: Stochastic Tools in Turbulence. Academic, New York NY, 194 p. (1978)Google Scholar
  12. 12.
    Lumley, J.L.: Computational modeling of turbulence flows. Adv. Appl. Mech. 18, 123–17 (1983)Google Scholar
  13. 13.
    McComb, W.D.: The Physical of Fluid Turbulence. Clarendon, Oxford, 572 p. (1990)Google Scholar
  14. 14.
    Monin, A.S. and Yaglom, A.M.: Statistical Fluid Mechanics, Vol. 1 (ed. Lumley, J.) MIT, Cambridge, MA, 769 p. (1971)Google Scholar
  15. 15.
    Monin, A.S. and Yaglom, A.M.: Statistical Fluid Mechanics, Vol. 2 (ed. Lumley, J.) MIT, Cambridge, MA, 874 p. (1975)Google Scholar
  16. 16.
    Munk, W.H.: On the wind-driven ocean circulation. J. Metereol. 7, 79 (1950)Google Scholar
  17. 17.
    Piquet, J.: Turbulence Flows, Models and Physics. Springer, Berlin, 761 p. (1999)Google Scholar
  18. 18.
    Prandtl, L.: Bericht über Untersuchungen zur ausgebildeten Turbulenz. Zeitschrift für angewandte Mathmatik und Mechanik (ZAMM) 5(2), 136–39 (1925)Google Scholar
  19. 19.
    Prandtl, L.: Neuere Ergebnisse der Turbulenzforschung. Zeitschr. VDI 77, 105–113 (1933)Google Scholar
  20. 20.
    Reynolds, O.: An experimental investigation of circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. A–174, 935–982 (1883)Google Scholar
  21. 21.
    Reynolds, O.: On the dynamical theory of turbulent incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. Lond. A 186, 123–164 (1894)Google Scholar
  22. 22.
    Rodi, W.: Examples of calculation methods for flow and mixing in stratified fluids. J. Geophys. Res. (C5), 92, 5305–5328 (1987)CrossRefGoogle Scholar
  23. 23.
    Rodi, W.: Turbulence Models and Their Application in Hydraulics. IAHR Monograph Series, A.A. Balkema, Rotterdam/Brookfield (1993)Google Scholar
  24. 24.
    Rotta, J.C.: Turbulente Strömungen, eine Einführung in die Theorie und ihre Anwendung.Teubner, Stuttgart, 267 p. (1972)Google Scholar
  25. 25.
    Sander, J.: Dynamical equations and turbulent closures in geophysics. Continuum Mech. Thermodyn. 10, 1–28 (1998)CrossRefGoogle Scholar
  26. 26.
    Svensson, U.: A mathematical model for the seasonal variation of the thermocline. Report 1002, Department of Water Resources Engineering, University of Lund, Sweden, 187 p. (1978)Google Scholar
  27. 27.
    Tennekes, H.J.L. and Lumley, J.L.: A First Course in Turbulence. MIT, Cambrdige, MA, 300 p. (1972)Google Scholar
  28. 28.
    Townsend, A.A.: The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge, 429 p. (1976)Google Scholar
  29. 29.
    Umlauf, L.: Turbulence Parameterization in Hydro-Biological Models for Natural Waters. Ph. D. Dissertation, Department of Mechanics, Darmstadt University of Technology, Darmstadt, Germany, 231 p. (2001)Google Scholar
  30. 30.
    Wang, Y.: Windgetriebene Strömungen in einem Rechteckbecken und im Bodensee. PhD thesis, Darmstadt University of Technology, Shaker Verlag, Aachen. ISBN 3-8265-1381-9, 432 p. (1996)Google Scholar
  31. 31.
    Weis, J.: Ein Algebraisches Reynolds-Spannungs-Modell. Ph. D. Dissertation, Department of Mechanics, Darmstadt University of Technology, Darmstadt, Germany, 111 p. (2001)Google Scholar
  32. 32.
    Wilcox, D.C.: Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988)CrossRefGoogle Scholar
  33. 33.
    Wilcox, D.C.: Tturbulence Modeling for CFD. DCW Industries, Inc., La Cañada, California, 2nd Edition (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.ETH Zürich, c/o Versuchsanstalt für Wasserbau Hydrologie und GlaziologieZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.Russian Academy of Sciences, P.P. Shirshov Institute of OceanologyKaliningradRussia

Personalised recommendations