Study of Lagrangian Characteristic times Using Direct Numerical Simulation of Turbulence

  • C. H. Lee
  • K. Squires
  • J. P. Bertoglio
  • J. Ferziger


Direct numerical simulations and large eddy simulations of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed time scales are compared with the spectral time scales that are frequently used in Eddy Damped Quasi-Normal Markovian calculations of the spectrum. The time scale models are rather good at high wavenumber and the results point to directions for improvement of the time scales at low wavenumber.


Large Eddy Simulation Direct Numerical Simulation Isotropic Turbulence Direct Simulation Inertial Subrange 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    von Karman, T.: The fundamentals of the statistical theory of turbulence. J. Aero. Sci. 4, 131 (1937)MATHGoogle Scholar
  2. 2.
    Heisenberg, W.: Zur Statistischen Theorie der Turbulenz. Z. Phys. 124, 628 (1948)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Obukhov, A. M.: Spectral energy distribution in a turbulent flow. Dokl. Akad. Nauk SSSR 32, 22 (1941)Google Scholar
  4. 4.
    Millionshikov, M. D.: Decay of homogeneous isotropic turbulence in a viscous incompressible fluid. Dokl. Akad. Nauk SSSR 22, 236 (1939)Google Scholar
  5. 5.
    Kraichnan, R. H.: The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497 (1959)MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Ogura, Y.: A consequence of the zero fourth order cumulant approximation in the decay of isotropic turbulence. J. Fluid Mech. 16, 33 (1962)ADSCrossRefGoogle Scholar
  7. 7.
    O’Brien, E. F., Francis, G. C.: A consequence of the zero fourth order cumulant approximation. J. Fluid Mech. 13, 369 (1962)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Orszag, S. A.: Analytical theories of turbulence. J. Fluid Mech. 41, 363 (1970)ADSMATHCrossRefGoogle Scholar
  9. 9.
    Kolmogoroff, A. N.: Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 26, 6 (1941)MathSciNetGoogle Scholar
  10. 10.
    Pouquet, A., Lesieur, M., Andre, J. C., Basdevant, C.: Evolution of high Reynolds number two dimensional turbulence. J. Fluid Mech. 72, 305 (1975)ADSMATHCrossRefGoogle Scholar
  11. 11.
    Lesieur, M.: Turbulence in Fluids: Stochastic and Numerical Modeling (Nijhoff, Dordrecht 1987)CrossRefGoogle Scholar
  12. 12.
    Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full- and narrow-band velocity signals in grid generated isotropic turbulence. J. Fluid Mech. 25, 273 (1971)ADSCrossRefGoogle Scholar
  13. 13.
    Yakhot, V., Orszag, S. A.: Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1, 3 (1986)MathSciNetMATHGoogle Scholar
  14. 14.
    Kraichnan, R. H.: Kolmogoroff’s constant and local interactions. Phys. Fluids 30, 1583 (1987)ADSCrossRefGoogle Scholar
  15. 15.
    Kraichnan, R. H. An interpretation of the Yakhof-Orszag theory, Phys. Fluids. 30, 2400 (1987) (to be published)ADSMATHCrossRefGoogle Scholar
  16. 16.
    Kaneda, Y.: Renormalized expansions in the theory of turbulence with the use of Lagrangian position function. J. Fluid Mech. 107, 131 (1981)ADSCrossRefGoogle Scholar
  17. 17.
    Herring, J. R.: Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859 (1974)ADSMATHCrossRefGoogle Scholar
  18. 18.
    Bertoglio, J. P.: “Etude d’une Turbulence Anisotrope; Modelisation de Sous-Maille et Approche Statistique;” Thèse d’Etat, Universite C. Bernard, Lyon (1986)Google Scholar
  19. 19.
    Rogallo, R. S.: Numerical experiments in homogeneous turbulence. TM-81315, NASA Ames Research Center (1981)Google Scholar
  20. 20.
    Squires, K., Eaton, J.: to be publishedGoogle Scholar
  21. 21.
    Chollet, J. P., Lesieur, M.: Parametrization of small scales of three dimensional isotropic turbulence utilizing spectral closures. J. Atm. Sci. 38, 2747 (1981)ADSCrossRefGoogle Scholar
  22. 22.
    Yeung, P. K., Pope, S. B.: “Lagrangian velocity statistics obtained from direct numerical simulations of homogeneous turbulence,” Sixth Symposium on Turbulent Shear Flows, Toulouse (1987)Google Scholar
  23. 23.
    Riley, J. J., Patterson, G. S.: Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids 17, 292 (1974)ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • C. H. Lee
    • 1
  • K. Squires
    • 2
  • J. P. Bertoglio
    • 1
  • J. Ferziger
    • 2
  1. 1.Laboratoire de Mécanique des Fluides et d’AcoustiqueEcole Central de LyonEcullyFrance
  2. 2.Department of Mechanical EngineeringStanford UniversityStanfordUSA

Personalised recommendations