Journal of Mathematical Sciences

, Volume 88, Issue 2, pp 134–141 | Cite as

The problem of justifying Kolmogorov's conjectures in the stochastic theory of turbulence

  • L. Ts. Adzhemyan
  • N. V. Antonov
  • A. N. Vasil'ev
  • M. M. Perekalin
Article
Received:
  • 27 Downloads

Abstract

The problem of justification of Kolmogorov's phenomenological conjectures by the methods of quantum field theory is discussed in the stochastic theory of well-developed turbulence. Bibliography: 24 titles.

Keywords

Field Theory Quantum Field Theory Stochastic Theory 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. N. Popov,Continual Integrals in Quantum Field Theory and Statistical Physics [in Russian], Atomizdat, Moscow (1976).Google Scholar
  2. 2.
    N. P. Konopleva and V. N. Popov,Gauge Fields [in Russian], Atomizdat, Moscow (1980).Google Scholar
  3. 3.
    A. S. Monin and A. M. Yaglom,Statistical Hydromechanics, Part 2 [in Russian], Nauka, Moscow (1967).Google Scholar
  4. 4.
    W. D. McComb,The Physics of Fluid Turbulence, Clarendon Press, Oxford (1990).Google Scholar
  5. 5.
    C. De Dominicis and P. C. Martin,Phys. Rev.,A19, 419 (1979).Google Scholar
  6. 6.
    L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev,Zh. Eksp. Teor. Fiz.,95, 1272 (1989).Google Scholar
  7. 7.
    J. Zinn-Justin,Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford (1989).Google Scholar
  8. 8.
    B. B. Kadomtsev,Questions of the Theory of Plasma [in Russian], Atomizdat, Moscow (1964).Google Scholar
  9. 9.
    R. A. Antonia, B. R. Satyaprakash, and A. K. M. F. Hussian,J. Fluid Mech.,119, 55 (1982); F. Anselment, Y. Gagne, E. Hopfinger, and R. A. Antonia,J. Fluid Mech. 140, 63 (1984).Google Scholar
  10. 10.
    V. R. Kuznetsov and V. A. Sabel'nikov,Turbulence and Combustion [in Russian], Nauka, Moscow (1966); V. R. Kuznetsov, A. A. Praskovskii, and V. A. Sabel'nikov,Izv. Akad. Nauk SSSR, Mekh. Zhidk., Gaza, No. 6, 51 (1988).Google Scholar
  11. 11.
    M. S. Borgas,Phys. Fluids,A4(9), 2055 (1992).MATHGoogle Scholar
  12. 12.
    L. Ts. Adzhemyan, A. N. Vasil'ev, and Yu. M. Pis'mak,Teor. Mat. Fiz.,57, 286 (1993).MathSciNetGoogle Scholar
  13. 13.
    J.-D. Fournier and V. Frish,Phys. Rev.,A28, 1000 (1983).Google Scholar
  14. 14.
    L. Ts. Adzhemyan, A. N. Vasil'ev, and M. Gnatich,Teor. Mat. Fiz.,74, 180 (1988).MathSciNetGoogle Scholar
  15. 15.
    N. V. Antonov,Zap. Nauch. Semin. LOMI,169, 18 (1988).MATHGoogle Scholar
  16. 16.
    N. V. Antonov,Vestnik SPbGU, Ser. Fiz., Khim.,4, 6 (1992).Google Scholar
  17. 17.
    L. Ts. Adzhemyan, N. V. Antonov, and T. L. Kim,Teor. Mat. Fiz.,100, 18 (1994).MathSciNetGoogle Scholar
  18. 18.
    V. S. L'vov,Phys. Rep. 207, 1 (1991).CrossRefMathSciNetGoogle Scholar
  19. 19.
    N. V. Antonov,Zh. Eksp. Teor. Fiz.,105, 614 (1994).Google Scholar
  20. 20.
    N. V. Antonov,Zap. Nauch. Semin. LOMI,189, 15 (1991).MATHGoogle Scholar
  21. 21.
    N. V. Antonov,Vestnik SPbGU, Ser. Fiz., Khim.,3, 3 (1992).MathSciNetGoogle Scholar
  22. 22.
    Adzhemyan L. Ts. and Antonov, N. V.,Vestnik SPbGU, Ser. Fiz., Khim.,2, (1994).Google Scholar
  23. 23.
    V. Yakhot, Z.-S. She, and S. A. Orszag,Phys. Fluids,A1(2), 289 (1989).MathSciNetGoogle Scholar
  24. 24.
    V. Yakhot and L. M. Smith,J. Sci. Comp.,7, 35 (1992).MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • L. Ts. Adzhemyan
  • N. V. Antonov
  • A. N. Vasil'ev
  • M. M. Perekalin

There are no affiliations available

Personalised recommendations