Advertisement

On the Scale-Invariant Theory of Developed Hydrodynamic Turbulence Kolmogorov Type

  • Victor S. L’vov
Part of the NATO ASI Series book series (NSSB, volume 225)

Abstract

The modern statistical theory of hydro dynamic turbilience goes back to the papers by Kraichnan and Wyld [1,2], who suggested to simulate excitation of stationary space-homogeneous developed hydrodynamic turbulence with the help of a space-distributed variable force f(r,t). According to the Kolmogorov-Obukhov’s universality hypothesis [3,4] one can believe that in the limit of a large Reynolds number, the properties of fine-scale part of the turbulence (in the inertial range) will not depend on the way of turbulence excitation, i.e. of the type of the boundary conditions for the liquid flow or characteristics of the exciting force f̄(r̄,t). Therefore, one can suppose that the force f̄ is a random force with a Gaussian statistics, it does not excite the mean flow: <f̄(r̄,t)> = 0, and its pair correlator D depends only on the coordinates and time difference:

Keywords

Inertial Range Exciting Force Euler Velocity Lagrange Velocity Kolmogorov Turbulence 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kraichnan R.H. — J.Fluid Mech., 1959, v. 6, p. 497.MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Wyld H.W.-Ann. Phys., 1961, v.14, p.143.MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Kolmogorov A.N. —DAN SSSR, 1941, v.30. p.229Google Scholar
  4. 3a.
    Kolmogorov A.N. DAN SSSR, 1941, v.32. p.19Google Scholar
  5. 3b.
    Obukhov A.M. DAN SSSR, 1941, v.32. p.22Google Scholar
  6. 3c.
    Kolmogorov A.N. AN SSSR, Ser.geograph. i geophizika, 1941, v.5, p. 443.Google Scholar
  7. 4.
    Monin A.S., Yaglom A.M. Statisticheskaya gidromekhanica, part 2, M.: Nauka, 1967.Google Scholar
  8. 5.
    Foster D., Nelson D.R., Stephen M.J. — Phys. Rev., 1977, V.A16. p.732.ADSGoogle Scholar
  9. 6.
    Martin P.C., Siggia E.D., Rose H.A. — Phys. Rev. A, 1972, V.8. p.423ADSCrossRefGoogle Scholar
  10. 6a.
    DeDominics C., Martin P.C. — Phys. Rev., 1979, V.A19, p.419.ADSGoogle Scholar
  11. 7.
    Adzhemyan L.Ts., Vasiljev A.N., Pis’mak Yu.M. — TMF, 1983.v.57. N 2, p.268–281.MATHGoogle Scholar
  12. 8.
    L’vov V.S. To the theory of developed hydrodynamic turbulence. Preprint IA&E SO AN SSSR, 1977, N 53 (in Russian).Google Scholar
  13. 9.
    Kraichnan R.H.-Proc.Symp.Dynamics of Fluids and Plasma. N.Y.: Ac.Press, 1967,Google Scholar
  14. 9a.
    Kraichnan R.H J. Fluid Mech., 1977, v.83.P.349MathSciNetADSMATHCrossRefGoogle Scholar
  15. Kraichnan R.H Phys.Fluid, 1965, v.8, p.575, 1966MathSciNetADSCrossRefGoogle Scholar
  16. Kraichnan R.H Phys.Fluid v.9, p.728.Google Scholar
  17. 10.
    Belinicher V.I., L’vov V.S. Scale-invariant theory of developed hydrodynamic turbulence.Preprint IA&ESO Ac.Sci. USSR, N 333, 1986 (in Russian), N 358.1987 (in English), Zh.Eksp, Teor.Fis., 1987, V.93.N 2(8), pp.533–551.ADSGoogle Scholar
  18. 11.
    A. V. Tur, V.V. Yanovsky. On the theory of developed turbu -lence in incompressible fluid.Preprint of Space Researched Institute USSR Ac.Sci. N1203, Moscow 1986.Google Scholar
  19. 12.
    Tur A.V., Yanovsky V.V., Moiseev S.S. Proceeding of the International working group on nonlinear physics and turbulence, Kiev, 1983, p.1693Google Scholar
  20. 12.
    Tur A.V., Yanovsky V.V., Moiseev S.S. DAN SSSR, 1984.v. 279. p.96.Google Scholar
  21. 13.
    Sagdeev R.Z., Moiseev S.S., Tur A.V., Yanovsky V.V. — In “Nonlinear phenomena in plasma phys. and hydrodinamics”, ed. R.Z. Sagdeev, Mir Publ. 1986, p.137.Google Scholar
  22. 14.
    Zakharov V.E., L’vov V.S. — IVUZ, Radiofizika, 1975, XVIII, pp. 1470–1487.ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Victor S. L’vov
    • 1
  1. 1.Siberian Branch of Academy of ScienceInstitute of Automation and ElectrometryNovosibirskU.S.S.R.

Personalised recommendations