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Spatial dependence of correlation functions in the decay problem for a passive scalar in a large-scale velocity field

  • S. S. Vergeles
Statistical, Nonlinear, and Soft Matter Physics

Abstract

Statistical characteristics of a passive scalar advected by a turbulent velocity field are considered in the decay problem with a low scalar diffusivity κ (large Prandtl number v/κ, where v is kinematic viscosity). A regime in which the scalar correlation length remains smaller than the velocity correlation length is analyzed. The equal-time correlation functions of the scalar field are found to vary according to power laws and have angular singularities reflecting locally layered distribution of the scalar in space.

PACS numbers

05.20.Jj 47.27.Gs 47.27.-i 

References

  1. 1.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, 3rd ed. (Nauka, Moscow, 1986; Pergamon, New York, 1987).Google Scholar
  2. 2.
    A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics, 2nd ed. (Gidrometeoizdat, St. Petersburg, 1996; MIT Press, Cambridge, 1975).Google Scholar
  3. 3.
    A. N. Kolmogorov, Dokl. Akad. Nauk 32, 16 (1941).zbMATHGoogle Scholar
  4. 4.
    U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1995; Fazis, Moscow, 1998).zbMATHGoogle Scholar
  5. 5.
    R. H. Kraichnan and D. Montgomery, Rep. Prog. Phys. 43, 547 (1980).MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    R. H. Kraichnan, Phys. Fluids 7, 1723 (1964); Adv. Math. 16, 305 (1975).zbMATHMathSciNetCrossRefADSGoogle Scholar
  7. 7.
    G. Falkovich and V. Lebedev, Phys. Rev. E 50, 3883 (1994); 49, 1800 (1994).MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).zbMATHMathSciNetCrossRefADSGoogle Scholar
  9. 9.
    A. Groisman and V. Steinberg, Nature 405, 53 (2000).CrossRefADSGoogle Scholar
  10. 10.
    R. H. Kraichnan, Phys. Fluids 11, 945 (1968).zbMATHMathSciNetCrossRefADSGoogle Scholar
  11. 11.
    A. P. Kazantsev, Zh. Éksp. Teor. Fiz. 53, 1806 (1967) [Sov. Phys. JETP 26, 1031 (1967)].Google Scholar
  12. 12.
    G. Falkovich, K. GawOpen image in new windowdzki, and M. Vergassola, Rev. Mod. Phys. 73, 913 (2001).CrossRefADSGoogle Scholar
  13. 13.
    M. Chertkov and V. Lebedev, Phys. Rev. Lett. 90, 034501 (2003).Google Scholar
  14. 14.
    M. Chaves, G. Eyink, U. Frisch, and M. Vergassola, Phys. Rev. Lett. 86, 2305 (2001).CrossRefADSGoogle Scholar
  15. 15.
    E. Balkovsky and A. Fouxon, Phys. Rev. E 60, 4164 (1999).MathSciNetCrossRefADSGoogle Scholar
  16. 16.
    M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Int. J. Mod. Phys. B 10, 2273 (1996); Phys. Rev. E 51, 5609 (1995).CrossRefADSGoogle Scholar
  17. 17.
    R. Ellis, Entropy, Large Deviations and Statistical Mechanics (Springer, Berlin, 1985).zbMATHGoogle Scholar
  18. 18.
    S. S. Girimaji and S. B. Pope, J. Fluid Mech. 220, 427 (1990).CrossRefADSGoogle Scholar
  19. 19.
    I. Goldhirsch, P.-L. Sulem, and S. A. Orszag, Physica D (Amsterdam) 27, 311 (1987).zbMATHMathSciNetADSGoogle Scholar
  20. 20.
    Y. Amarouchene and H. Kellay, Phys. Rev. Lett. 93, 214504 (2004).Google Scholar
  21. 21.
    X.-L. Wu, B. Martin, H. Kellay, and W. I. Goldburg, Phys. Rev. Lett. 75, 236 (1994).CrossRefADSGoogle Scholar
  22. 22.
    G. Falkovich, I. Kolokolov, V. Lebedev, and A. Migdal, Phys. Rev. E 54, 4896 (1996).CrossRefADSGoogle Scholar
  23. 23.
    I. V. Kolokolov and K. S. Turitsyn, Zh. Éksp. Teor. Fiz. 121, 1219 (2002) [JETP 94, 1193 (2002)]Google Scholar
  24. 24.
    E. Balkovsky, M. Chertkov, I. Kolokolov, and V. Lebedev, Phys. Rev. E 52, 4924 (1995); Pis’ma Zh. Éksp. Teor. Fiz. 61, 1012 (1995) [JETP Lett. 61, 1049 (1995)].MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    E. Balkovsky, G. Falkovich, V. Lebedev, and M. Lysiansky, Phys. Fluids 11, 2269 (1999).MathSciNetCrossRefADSzbMATHGoogle Scholar
  26. 26.
    M.-C. Jullien, P. Castiglione, and P. Tabeling, Phys. Rev. Lett. 85, 3636 (2000).CrossRefADSGoogle Scholar
  27. 27.
    A. Gamba and I. V. Kolokolov, J. Stat. Phys. 94, 759 (1999).zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • S. S. Vergeles
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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