Recent Approaches in Large-Eddy Simulations of Turbulence

  • M. Lesieur
Part of the Centre de Physique des Houches book series (LHWINTER, volume 5)

Abstract

The general framework of large-eddy simulations (LES) is first presented with Smagorinsky’s model [1]. Afterwards Kraichnan’s spectral eddy-viscosity[2] is introduced, and how it can be handled for LES purposes in isotropic turbulence. The spectral eddy viscosity is generalized to a spectral eddy diffusivity. Using the nonlocal interaction theory, the backscatter issue is discussed, and a generalization of spectral eddy coefficients is presented allowing to account for non-developed turbulence in the subgridscales, the spectral-dynamic model. Utilization of these spectral models in physical space is envisaged in terms of respectively the structure-function and hyperviscosity models. Three applications of these models to shear flows are considered, namely the plane mixing layer, the channel flow and the backward-facing step, with statistical results and information on the topology of coherent vortices and structures. In the mixing layer case in particular, how longitudinal vorticity may be stretched into hairpins of spanwise wave length corresponding to Pierrehumbert and Widnall’s translative instability[3] is explained.

Keywords

Combustion Vortex Vorticity Expense Peri 

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References

  1. [1]
    Smagorinsky J., Mon. Weath. Rev. 91 (3) (1963) 99.Google Scholar
  2. [2]
    Kraichnan R.H., J. Atmos. Sci. 33 (1976) 1521.ADSCrossRefGoogle Scholar
  3. [3]
    Pierrehumbert R.T., Widnall S.E., J . Fluid Mech. 114 (1982) 59.ADSMATHCrossRefGoogle Scholar
  4. [4]
    Lesieur M.,Turbulence in fluids, third edition,Kluwer Academic Publishers (1997).Google Scholar
  5. [5]
    Lesieur M., Métais O., Ann. Rev. Fluid Mech. 28 (1996) 45.Google Scholar
  6. [6]
    Germano M., J. Fluid Mech. 238 (1992) 325.MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod (1969).Google Scholar
  8. Chollet J.P., Lesieur M., J. Atmos. Sci. 38 (1981) 2747.Google Scholar
  9. [9]
    Chollet J.P., Lesieur M., La Météorologie 29–30 (1982) 183.Google Scholar
  10. [10]
    Lesieur, M., Rogallo R., Phys. Fluids A 1 (1989) 718.Google Scholar
  11. [11]
    Lesieur M., Métais O., Rogallo R.,, C.R. Acad. Sci. Paris Ser I I 308 (1989) 1395.Google Scholar
  12. [12]
    Métais O., Lesieur M. J. Atmos. Sci. 43 (1986) 857.ADSCrossRefGoogle Scholar
  13. [13]
    Métais O., Lesieur M., J. Fluid Mech. 239 (1992) 157.Google Scholar
  14. [14]
    Lesieur M., Schertzer D., Journal de Mécanique 17 (1978) 609.Google Scholar
  15. [15]
    Lamballais E., Simulations numériques de la turbulence dans un canal plan tournant. Thèse de l’Institut National Polytechnique de Grenoble (1995).Google Scholar
  16. [16]
    Lamballais E., Lesieur M., Métais, O., C. R. Acad. Sci. Paris Ser IIb 323 (1996) 95.Google Scholar
  17. [17]
    Leslie D.C., Quarini G.L., J. Fluid Mech. 91 (1979) 65.ADSMATHCrossRefGoogle Scholar
  18. [18]
    Ducros F., Comte P., Lesieur M., In: Turbulent Shear Flows IX. Springer-Verlag, (1995) 283.Google Scholar
  19. [19]
    David E., Modélisation des écoulements compressibles et hypersoniques: une approche instationnaire. Thèse, Institut National Polytechnique de Grenoble (1993).Google Scholar
  20. [20]
    Ducros F., Simulations numériques directes et des grandes échelles de couches limites compressibles. Thèse, Institut National Polytechnique de Grenoble (1995).Google Scholar
  21. [21]
    Ducros F., Comte P., Lesieur, M., J. Fluid Mech. 326 (1996) 1.ADSMATHCrossRefGoogle Scholar
  22. [22]
    Herbert T., Ann. Rev. Fluid Mech. 20 (1988) 487.ADSCrossRefGoogle Scholar
  23. [23]
    Garnier E., Métais O., Lesieur, M., C.R. Acad. Sci. Paris Ser II b 323 (1996) 161.MATHGoogle Scholar
  24. [24]
    Silvestrini, J., Simulation des grandes échelles des zones de mélange: application à la propulsion solide des lanceurs spatiaux. Thèse de l’Institut National Polytechnique de Grenoble (1996).Google Scholar
  25. [25]
    Konrad J.H., An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Ph.D. Thesis, California Institute of Technology (1976).Google Scholar
  26. [26]
    Bernal L.P., Roshko A., J. Fluid Mech. 170 (1986) 499.ADSCrossRefGoogle Scholar
  27. [27]
    Corcos G.M., Lin S.J., J. Fluid Mech. 139 (1984) 67.ADSMATHCrossRefGoogle Scholar
  28. [28]
    Neu J.C., J. Fluid Mech. 143 (1984) 253.ADSMATHCrossRefGoogle Scholar
  29. [29]
    Comte P., Lesieur M., In: H.K. Moffatt (ed.) Topological Fluid Dynamic. Cambridge University Press (1989) 649.Google Scholar
  30. [30]
    Comte P., Fouillet Y., Gonze M.A., Lesieur M., Métais O., Normand X., Large-eddy simulations of free-shear layers. In: O. Métais and M. Lesieur (eds.) Turbulence and coherent structures. Kluwer Academic Publishers (1991) pp. 45–73.Google Scholar
  31. [31]
    Comte P., Lesieur M., Lamballais E., Phys. Fluids A 4 (1992) 2761.Google Scholar
  32. [32]
    Piomelli U., Phys. Fluids A 5 (1993) 1484.ADSCrossRefGoogle Scholar
  33. [33]
    Antonia R. A., Teitel M., Kim J., Browne L.W.B., J. Fluid Mech. 236 (1992) 579.ADSCrossRefGoogle Scholar
  34. Eaton J.K., Johnston J.P., Stanford University, Rep. MD-39 (1980).Google Scholar
  35. [35]
    Le H., Moin P., Stanford University, Rep. TF-58 (1994).Google Scholar
  36. [36]
    Silveira-Neto A., Grand D., Métais O., Lesieur M., J. Fluid Mech. 256 (1993) 1.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • M. Lesieur
    • 1
  1. 1.LEGI/IMGGrenoble-Cedex 09France

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