Experimental Check of Infinite Divisibility for the Velocity Cascade in Developed Turbulence

  • A. Naert
  • B. Chabaud
  • B. Hébral
  • B. Castaing
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 36)


Interest raised recently about Infinite Divisibility [1, 2] of dissipation logarithm distributions (IDD) and Extended Self Similarity (ESS) [3] of velocity difference moments [4]. However the largest confusion exists about experimental tests. The relation between IDD and ESS lie on the Kol-mogorov refined hypothesis [5] whose verification is not exempt of problems [6, 7]. On the other hand, the multifractal approach [8] and others focused on a distribution of local velocity amplitudes independently of the dissipation field. Some generalizations [9] have been shown [10] to yield both ESS and infinite divisibility for the distributions of logarithms of these velocity amplitudes (the last one hereafter refered as ID).


Reynolds Number High Reynolds Number Velocity Amplitude Infinite Divisibility Levy Distribution 
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  1. 1.
    Saito, Y., J. Phys. Soc. Jpn 61 (1992) 403.ADSCrossRefGoogle Scholar
  2. 2.
    She, Z.-S. and Leveque, E., Phys. Rev. Lett. 72 (1994) 336; She, Z.-S. and Waymire, E.C., Phys. Rev. Lett. 74 (1995) 262.ADSCrossRefGoogle Scholar
  3. 3.
    Benzi, R., Ciliberto, S., Baudet, C., Tripiccione, R., Massaioli, F., Succi, S., Phys. Rev. E 48 (1993) R29.ADSCrossRefGoogle Scholar
  4. 4.
    Novikov, E.A., Phys. Rev. E 50 (1994) R3303; Dubrulle, B., Phys. Rev. Lett. 73 (1994) 959; Chen, S. and Cao, N., Phys. Rev. E 52 (1995) R5757; Pedrizzetti, Novikov, E.A., Praskovsky, A.A., Phys. Rev. E 53 (1996) 475; Nelkin, M., Advances in Physics 43 (1994) 143.ADSCrossRefGoogle Scholar
  5. 5.
    Kolmogorov, A.N., J.F.M. 13 (1962) 82; Obukhov, A.M., J.F.M. 13 (1962) 77.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Stolovitzky, G., Sreenivasan, K.R., Reviews Mod. Phys. 66 (1994) 229; Borne, V., Orszag, S., Phys. Rev. E 53 (1996) R21.ADSCrossRefGoogle Scholar
  7. 7.
    Gagne, Y., Marchand, M., Castaing, B., J. Phys. II (France) 4 (1994) 1.CrossRefGoogle Scholar
  8. 8.
    Parisi, G. and Frisch, U., in “Turbulence and PredictabilityVarenna”, Summer School, M. Ghol, R. Benzi, G. Parisi Eds (North-Holland, Amsterdam 1985) p. 84.Google Scholar
  9. 9.
    Castaing, B., Gagne, Y., Hopfinger, E.J., Physica D 46 (1990) 177; Castaing, B., Gagne, Y., in “Turbulence in Spatially Extended Systems”R. Benzi, C. Basdevant, S. Ciliberto Eds (Les Houches 1993).ADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Castaing, B., Dubrulle, B., J. Phys. II (France) 5 (1995) 895; Castaing, B., J. Phys. II (France) 6 (1996) 105.CrossRefGoogle Scholar
  11. 11.
    Monin, A.S., Yaglom, A.M., in “Statistical Fluid Mechanics” (MIT Press, Cambridge, Massachussetts 1975).Google Scholar
  12. 12.
    Feller, W., in “An Introduction to Probability Theory and its Applications” (Wiley, New York 1971) Vol. 2.zbMATHGoogle Scholar
  13. 13.
    Schertzer, D., Lovejoy, S., Schmitt, F., in “Small Scale Structures in 3D and MHD Turbulence”, P.L. Sulem, M. Meneguzzi, A. Pouquet eds (Springer 1995).Google Scholar
  14. 14.
    Chabaud, B., Naert, A., Peinke, J., Chillà, F., Castaing, B., Hébral, B., Phys. Rev. Lett. 73 (1994) 3227.ADSCrossRefGoogle Scholar
  15. 15.
    Castaing, B., Hébral, B., Chabaud, B., Rev. Scient. Inst. 63 (1992) 4167.ADSCrossRefGoogle Scholar
  16. 16.
    Castaing, B., Gagne, Y., Marchand, M., Physica D 68 (1993) 387.ADSzbMATHCrossRefGoogle Scholar
  17. 17.
    Benzi, R., Bifferale, L., Ciliberto, S., Struglia, M.V., Tripiccione, L., Physica D, in press (1996).Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • A. Naert
    • 1
  • B. Chabaud
    • 1
  • B. Hébral
    • 1
  • B. Castaing
    • 1
  1. 1.CRTBT, laboratoire associé à l’UJFCNRSGrenoble-Cedex 9France

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