Advertisement

Theoretical and Mathematical Physics

, Volume 105, Issue 3, pp 1556–1565 | Cite as

Renormalization group approach and short-distance expansion in theory of developed turbulence: Asymptotics of the triplex equal-time correlation function

  • L. Ts. Adzhemyan
  • S. V. Borisenok
  • V. I. Girina
Article

Abstract

Asymptotics of the triplex equal-time correlation function for the turbulence developed in incompressible fluids in the region of widely separated wave vector values is investigated using the renormalization group approach and short-distance expansion. The problem of the most essential composite operators contributing to these asymptotics is examined. For this purpose, the critical dimensions of a family of composite quadratic tensor operators in the velocity gradient are found. Considered in the one-loop approximation, the contribution of these operators turns out to be less substantial (although not significantly) than the contribution of the linear term. The derived asymptotics of the triplex correlator coincide in form with that predicted by the EDQNM approximation.

Keywords

Correlation Function Wave Vector Renormalization Group Velocity Gradient Linear Term 
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.
    C. De Dominicis and P. C. Martin,Phys. Rev.,A29, 419–422 (1979).Google Scholar
  2. 2.
    L. Ts. Adzhemyan, A. N. Vasiliev, and Yu. M. Pismak,Teor. Mat. Fiz.,57, 268–281 (1983).Google Scholar
  3. 3.
    L. Ts. Adzhemyan, A. N. Vasiliev, and M. Gnatich,Teor. Mat. Fiz.,74, 180–191 (1988).Google Scholar
  4. 4.
    L. Ts. Adzhemyan, N. V. Antonov, and T. L. Kim,Teor. Mat. Fiz.,100, 382–401 (1994).Google Scholar
  5. 5.
    J. Zinn-Justen,Quantum Field Theory and Critical Phenomena, Clarendon, Oxford (1989).Google Scholar
  6. 6.
    L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasiliev,Zh. Eksp. Teor. Fiz.,95, 1272–1288 (1989).Google Scholar
  7. 7.
    V. I. Belinicher and V. S. L'vov,Zh. Eksp. Teor. Fiz.,93, 533–551 (1987).Google Scholar
  8. 8.
    V. L'vov and G. Falkovich,Phys. Rev. 1992,46, 4762–4772.Google Scholar
  9. 9.
    S. A. Orszag, “Lectures on the statistical theory of turbulence,” in:Fluid Dynamics (R. Balian, ed.), Les Houches (1973).Google Scholar
  10. 10.
    L. Ts. Adzhemyan and M. Yu. Nalimov,Teor. Mat. Fiz.,91, 294–308 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • L. Ts. Adzhemyan
    • 1
  • S. V. Borisenok
    • 1
  • V. I. Girina
    • 1
  1. 1.State UniversitySt. Petersburg

Personalised recommendations