University in turbulence: An exactly solvable model

  • K. Gawedzki
  • A. Kupiainen
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 469)


Structure Function Zero Mode Gibbs Measure Eddy Diffusivity Integral Scale 
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.


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  1. 1.
    Phase transitions and critical phenomena. Vol. 6 eds. C. Doomb, M. S. Green. Academic Press, London 1976.Google Scholar
  2. 2.
    R. L. Dobrushin, R. Kotecký, S. Shlosman: The Wulff construction: a global shape from local interactions. AMS, Translations of Mathematical Monographs 104, Providence, Rhode Island 1992Google Scholar
  3. 3.
    J. Feldman, E. Trubowitz: The Flow of an Electron-Phonon System to the Superconducting State, Helv. Phys. Acta 64 (1991), 213–257MathSciNetGoogle Scholar
  4. 4.
    J. Fröhlich: Lectures, Schladming, 1995.Google Scholar
  5. 5.
    M. J. Feigenbaum: Qualitative Universality for a Class of Nonlinear Transformations. J. Stat. Phys. 19 (1978), 25–52CrossRefMathSciNetzbMATHADSGoogle Scholar
  6. 6.
    J. Bricmont, A. Kupiainen: Renormalizing Partial Differential Equations. Commun. Pure. Appl. Math. 47 (1994), 893–922MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    K. G. Wilson, J. Kogut: The Renormalization Group and the ∈-Expansion. Phys. Rep. 12 (1974), 75–200CrossRefADSGoogle Scholar
  8. 8.
    K. G. Wilson: The Renormalization Group and Critical Phenomena. Rev. Mod. Phys. 55 (1983), 583–600CrossRefADSGoogle Scholar
  9. 9.
    A. N. Kolmogorov: The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds' Numbers, C. R. Acad. Sci. URSS 30 (1941), 301–305Google Scholar
  10. 10.
    A. M. Obukhov: Structure of the Temperature Field in a Turbulent Flow. Izv. Akad. Nauk SSSR, Geogr. Geofiz. 13 (1949), 58–69Google Scholar
  11. 11.
    R. H. Kraichnan: Anomalous Scaling of a Randomly Advected Passive Scalar. Phys. Rev. Lett. 72 (1994), 1016–1019CrossRefADSGoogle Scholar
  12. 12.
    V. S. L'vov, I. Procaccia A. Fairhall: Anomalous Scaling in Fluid Dynamics: the Case of Passive Scalar. Phys. Rev. E50 (1994), 4684–4704CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    A. Majda: Explicit Inertial Range Renormalization Theory in a Model for Turbulent Diffusion. J. Stat. Phys. 73 (1993), 515–542CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. 14.
    M. Chertkov, G. Falkovich, I. Kolokolov, V. Lebedev: Normal and Anomalous Scaling of the Forth-Order Correlation Function of a Randomly Advected Passive Scalar Weizmann Institute preprint, chao-dyn/95030001Google Scholar
  15. 15.
    A. L. Fairhall, O. Gat, V. L'vov, I. Procaccia: Anomalous Scaling in a Model of Passive Scalar Advection: Exact Results. Weizmann Institute preprint 1995Google Scholar
  16. 16.
    R. H. Kraichnan, V. Yakhot, S. Chen: Scaling Relations for a Randomly Advected Passive Scalar Field, preprint 1995, submitted to Phys. Rev. Lett.Google Scholar
  17. 17.
    L. F. Richardson: Weather prediction by numerical process. Cambridge University Press: Cambridge 1922zbMATHGoogle Scholar
  18. 18.
    U. Frisch: Turbulence: the legacy of A. N. Kolmogorov, Cambridge University Press. Cambridge 1995, to appearzbMATHGoogle Scholar
  19. 19.
    P. C. Martin, E. D. Siggia, H. A. Rose: Statistical Dynamics of Classical Systems. Phys. Rev. A8 (1973), 423–437CrossRefADSGoogle Scholar
  20. 20.
    A. M. Polyakov: The Theory of Turbulence in Two Dimensions. Princeton University preprint, hep-th/9212145Google Scholar
  21. 21.
    V. I. Belinicher, V. S. L'vov: A Scale Invariant Theory of Fully Developed Hydrodynamic Turbulence. Sov. Phys. JETP 66 (1987), 303–313Google Scholar
  22. 22.
    V. S. L'vov: Scale Invariant Theory of Fully Developed Hydrodynamic Turbulence-Hamiltonian Approach. Phys. Rep. 207 (1991), 1–47CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    V. S. L'vov, I. Procaccia: Exact Resummation of the Theory of Hydrodynamic Turbulence. I. The Ball of Locality and Normal Scaling. Weizmann Institute preprint (1995), submitted to Phys. Rev. E Google Scholar
  24. 24.
    J. Glimm, D. H. Sharp: A Random Field Model for Anomalous Diffusion in Heterogeneous Porous Media. J. Stat. Phys. 62 (1991), 415–424CrossRefMathSciNetzbMATHADSGoogle Scholar
  25. 25.
    R. H. Kraichnan: Small-Scale Structure of a Scalar Field Convected by Turbulence. Phys. Fluids 11 (1968), 945–963CrossRefMathSciNetzbMATHADSGoogle Scholar
  26. 26.
    K. Gawędzki, A. Kupiainen: in preparationGoogle Scholar
  27. 27.
    C. E. Gutiérrez, G. S. Nolson: Bounds for the Fundamental Solution of Degenerate Parabolic Equations. Commun. Partial Diff. Eq. 13 (1988), 635–649zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • K. Gawedzki
    • 1
    • 2
  • A. Kupiainen
    • 1
    • 2
  1. 1.I.H.E.S., C.N.R.S.Bures-sur-YvetteFrance
  2. 2.Math. DepartmentHelsinki UniversityHelsinkiFinland

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