The Spectrum of Turbulence

  • Siegfried Grossmann


The clustered distribution of interstellar matter raised C.F. von Weizsäcker’s interest in turbulent flow with its nested vortex structures, its intermittent distribution of strongly active, dissipative turbulent bursts amidst more quiet regions, all this strongly fluctuating in time. Evidently many time scales are present, the smaller vortex structures circulating faster, being advected by the slower, larger ones. Also the spatial structures of the turbulent vortices or eddies display many scales. The prevailing impression of a turbulent flow field is its structural similarity on the various scales: zoomed smaller parts of the flow field look like larger ones, in a statistical sense. Such systems are properly described by power or scaling laws of the physical quantities of interest.


Structure Function Eddy Viscosity Energy Dissipation Rate Inertial Subrange Interstellar Matter 
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.
    A.N. Kolmogorov: Compt. Rend. Acad. Sc. (C. R. Acad. Nauk) USSR 30, 301 (1941)Google Scholar
  2. 2.
    A.M. Oboukhoff: Compt. Rend. Acad. Sc. (C. R. Acad. Nauk) USSR 32, 19 (1941)Google Scholar
  3. 3.
    C.F. von Weizsäcker: Z. Phys. 124, 614 (1948)ADSMATHCrossRefGoogle Scholar
  4. 4.
    W. Heisenberg: Z. Phys. 124, 628 (1948); Proc. R. Soc. (Lond) 195, 402 (1948)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    L. Onsager: Phys. Rev. 68, 286 (1945)Google Scholar
  6. 6.
    L.F. Richardson: Proc. R. Soc. (London) A110, 709 (1926)ADSCrossRefGoogle Scholar
  7. 7.
    L.F. Richardson: Beitr. Phys. Atm. 15, 24 (1929)Google Scholar
  8. 8.
    M.C. Jullien, J. Paret and P. Tabeling: Phys. Rev. Lett. 82, 2872 (1999)ADSCrossRefGoogle Scholar
  9. 9.
    S. Ott and J. Mann: J. Fluid Mech. 422, 207 (2000)ADSMATHCrossRefGoogle Scholar
  10. 10.
    G. Boffetta and I.M. Sokolov: Phys. Rev. Lett. 88, 094 501 (2002)Google Scholar
  11. 11.
    T. Ishihara and Y. Kaneda: preprint (2002)Google Scholar
  12. 12.
    S. Grossmann: Ann. d. Phys. (Leipzig) 47, 577 (1990)ADSMATHCrossRefGoogle Scholar
  13. 13.
    S. Grossmann and I. Procaccia: Phys. Rev. A29, 1358 (1984)ADSCrossRefGoogle Scholar
  14. 14.
    S. Grossmann and C. Wiele: Z. Phys. B 103, 469 (1997)CrossRefGoogle Scholar
  15. 15.
    S. Grossmann: preprint, Marburg 2002Google Scholar
  16. 16.
    L.D. Landau and E.M. Lifschitz: Hydrodynamik, 5th edition. Akademie Verlag, Berlin 1991Google Scholar
  17. 17.
    U. Frisch: Turbulence — The Legacy of A.N. Kolmogorov. Cambridge University Press, 1995Google Scholar
  18. 18.
    U. Frisch, P.-L. Sulem and M. Nelkin: J. Fluid Mech. 87, 719 (1978)ADSMATHCrossRefGoogle Scholar
  19. 19.
    G. Parisi and U. Frisch. In: M. Ghil, R. Benzi and G. Parisi (eds.): Turbulence and Predictability in Geophysical Fluid Dynamics. Proc. Intern. School of Physics “Enrico Fermi” 1983, Varenna, Italy. North Holland, Amsterdam 1985, pp. 84–87Google Scholar
  20. 20.
    This corresponds to 3 x 1022 cm; in [3] there is a misprint hereGoogle Scholar
  21. 21.
    H. Effinger and S. Grossmann: Z. Phys. B66, 289 (1987)CrossRefGoogle Scholar
  22. 22.
    H. Effinger and S. Grossmann: Selfsimilarity of Developed Turbulence. In: W. Göttinger (ed.): The Physics of Structure Formation: Theory and Experiment. Proc. Conference 27.10.-1.11. 1986, Tübingen, Germany. Springer, Berlin 1987, pp. 346–351CrossRefGoogle Scholar
  23. 23.
    S. Grossmann: Diffusion in Fully Developed Turbulence: A Random Walk on a Fractal Structure. In: L. Garrido (ed.): Fluctuations and Stochastic Phenomena in Condensed Matter. Proc. Sitges Conference 25–31 May, 1986. Lecture Notes in Physics 268. Springer, 1987, pp. 287–314Google Scholar
  24. 24.
    S. Grossmann and S. Thomae: Z. Phys. B49, 253 (1982)CrossRefGoogle Scholar
  25. 25.
    D. Daems, S. Grossmann, V.S. L’vov and I. Procaccia: Phys. Rev. E60, 6656 (1999) and chao-dyn/9811024Google Scholar
  26. 26.
    H. Effinger and S. Grossmann: Phys. Fluids AI, 1021 (1989)Google Scholar
  27. 27.
    G.K. Batchelor and A.A. Townsend: Proc. R. Soc. (London) A199, 238 (1949)ADSMATHCrossRefGoogle Scholar
  28. 28.
    A.M. Oboukhoff: J. Fluid Mech. 13, 77 (1962)MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    A.N. Kolmogorov: J. Fluid Mech. 13, 82 (1962)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    G. Falkovich, K. Gawgdzki and M. Vergassola: Rev. Mod. Phys. 73, 919 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    A. Noullez, G. Wallace, W. Lempert, R.B. Miles and U. Frisch: J. Fluid Mech. 339, 287 (1997)MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    S. Grossmann, D. Lohse and A. Reeh: Phys. Fluids 9, 3817 (1997)ADSCrossRefGoogle Scholar
  33. 33.
    B. Dhruva, Y. Tsuji and K.R. Sreenivasan: Phys. Rev E56, R4928 (1997)ADSGoogle Scholar
  34. 34.
    I. Arad, B. Dhruva, S. Kurien, V.S. L’vov, I. Procaccia and K.R. Sreenivasan: Phys. Rev. Lett. 81, 5330 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    I. Arad, L. Biferale, I. Mazzitelli and I. Procaccia: Phys. Rev. Lett. 82, 5040 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    I. Arad, V.S. L’vov and I. Procaccia: Phys. Rev. E59, 6753 (1999)MathSciNetADSGoogle Scholar
  37. 37.
    S. Grossmann, A. von der Heydt and D. Lohse: J. Fluid Mech 440, 381 (2001)ADSMATHCrossRefGoogle Scholar
  38. 38.
    S. Grossmann and D. Lohse: J. Fluid Mech. 407, 27 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  39. 39.
    S. Grossmann and D. Lohse: Phys. Rev. E66, 016305 (2002)Google Scholar
  40. 40.
    W. Heisenberg: Ann. d. Phys. (Leipzig) 74, 577 (1924)ADSCrossRefGoogle Scholar
  41. 41.
    L. Boberg and U. Brosa: Z. Natuiforsch. A43, 697 (1988)Google Scholar
  42. 42.
    L.N. Trefethen, A.E. Trefethen, S.C. Reddy and T.A. Driscol: Science 261, 578 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  43. 43.
    S. Grossmann: Rev. Mod. Phys. 72, 603 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Siegfried Grossmann

There are no affiliations available

Personalised recommendations