Passive scalar transport in peripheral regions of random flows

  • A. Chernykh
  • V. Lebedev
Statistical, Nonlinear, and Soft Matter Physics


We investigate statistical properties of the passive scalar mixing in random (turbulent) flows assuming its diffusion to be weak. Then at advanced stages of the passive scalar decay, its unmixed residue is primarily concentrated in a narrow diffusive layer near the wall and its transport to the bulk goes through the peripheral region (laminar sublayer of the flow). We conducted Lagrangian numerical simulations of the process for different space dimensions d and revealed structures responsible for the transport, which are passive scalar tongues pulled from the diffusive boundary layer to the bulk. We investigated statistical properties of the passive scalar and of the passive scalar integrated along the wall. Moments of both objects demonstrate scaling behavior outside the diffusive boundary layer. We propose an analytic scheme for the passive scalar statistics, explaining the features observed numerically.


Time Slot Diffusive Layer Peripheral Region Passive Scalar Diffusive Boundary Layer 
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  1. 1.
    A. M. Obukhov, Izv. Akad. Nauk. SSSR, Ser. Geogr. Geofiz. 13, 58 (1949).Google Scholar
  2. 2.
    S. Corrsin, J. Appl. Phys. 22, 469 (1951).MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 32, 16 (1941).zbMATHGoogle Scholar
  4. 4.
    K. R. Sreenivasan, Phys. Fluids 8, 189 (1996).MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Z. Warhaft, Annu. Rev. Fluid Mech. 32, 203240 (2000).MathSciNetCrossRefGoogle Scholar
  6. 6.
    J. Schumacher and K. R. Sreenivasan, Phys. Fluids 17, 125107 (2005).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    R. J. Miller, L. P. Dasi, and D. R. Webster, Exp. Fluids 44, 719 (2008).CrossRefGoogle Scholar
  8. 8.
    A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (Massachusetts Institute of Technology Press, Cambridge, Massachusetts, United States, 1975).Google Scholar
  9. 9.
    M. Lesieur, Turbulence in Fluids (Kluwer, Dordrecht, The Netherlands, 1997).zbMATHCrossRefGoogle Scholar
  10. 10.
    U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, New York, 1995).zbMATHGoogle Scholar
  11. 11.
    J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, United Kingdom, 1989).zbMATHGoogle Scholar
  12. 12.
    A. Groisman and V. Steinberg, Nature (London) 405, 53 (2000); A. Groisman and V. Steinberg, Phys. Rev. Lett. 86, 934 (2001); A. Groisman and V. Steinberg, Nature (London) 410, 905 (2001).ADSCrossRefGoogle Scholar
  13. 13.
    V. Kantsler and V. Steinberg, Phys. Rev. Lett. 95, 258101 (2005).ADSCrossRefGoogle Scholar
  14. 14.
    K. Gawedzki and A. Kupiainen, Phys. Rev. Lett. 75, 3608 (1995).CrossRefGoogle Scholar
  15. 15.
    B. Shraiman and E. Siggia, C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers 321, 279 (1995).zbMATHGoogle Scholar
  16. 16.
    M. Chertkov, G. Falkovich, I. Kolokolov, and V. Lebedev, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 52, 4924 (1995).MathSciNetCrossRefGoogle Scholar
  17. 17.
    B. I. Shraiman and E. D. Siggia, Nature (London) 405, 639 (2000).ADSCrossRefGoogle Scholar
  18. 18.
    G. Falkovich, K. Gawedzki, and M. Vergassola, Rev. Mod. Phys. 73, 913 (2001).MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. 19.
    T. Burghelea, E. Segre, and V. Steinberg, Phys. Fluids 19, 053104 (2007).ADSCrossRefGoogle Scholar
  20. 20.
    M. Chertkov and V. Lebedev, Phys. Rev. Lett. 90, 034501 (2003).ADSCrossRefGoogle Scholar
  21. 21.
    M. Chertkov and V. Lebedev, Phys. Rev. Lett. 90, 134501 (2003).ADSCrossRefGoogle Scholar
  22. 22.
    V. V. Lebedev and K. S. Turitsyn, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 69, 036301 (2004).MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    T. Burghelea, E. Segre, and V. Steinberg, Phys. Rev. Lett. 92, 164501 (2004).ADSCrossRefGoogle Scholar
  24. 24.
    M. Chertkov, I. Kolokolov, and V. Lebedev, Phys. Fluids 19, 101703 (2007).ADSCrossRefGoogle Scholar
  25. 25.
    E. Balkovsky, G. Falkovich, V. Lebedev, and M. Lysiansky, Phys. Fluids 11, 2269 (1999).MathSciNetADSzbMATHCrossRefGoogle Scholar
  26. 26.
    A. Chernykh and V. Lebedev, JETP Lett. 87(12), 682 (2008).ADSCrossRefGoogle Scholar
  27. 27.
    J.-Y. Vincont, S. Simoens, M. Ayrault, and J. M. Wallace, J. Fluid Mech. 424, 127 (2000).ADSzbMATHCrossRefGoogle Scholar
  28. 28.
    J. P. Crimaldi, M. B. Wiley, and J. R. Koseff, J. Turbul. 3, 014 (2002).MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    J. P. Crimaldi and J. R. Koseff, J. Fluid Mech. 6, 573 (2006).CrossRefGoogle Scholar
  30. 30.
    J. P. Crimaldi, J. R. Koseff, and S. G. Monismith, Phys. Fluids 18, 095102 (2006).ADSCrossRefGoogle Scholar
  31. 31.
    L. P. Dasi, F. Schuerg, and D. R. Webster, J. Fluid Mech. 588, 253277 (2007).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Automation and ElectrometrySiberian Branch of the Russian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  4. 4.Moscow Institute of Physics and TechnologyMoscowRussia

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