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Diffusion in turbulence
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  • Published: September 1996

Diffusion in turbulence

  • Albert Fannjiang1 &
  • George Papanicolaou2 

Probability Theory and Related Fields volume 105, pages 279–334 (1996)Cite this article

  • 173 Accesses

  • 46 Citations

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Summary

We prove long time diffusive behavior (homogenization) for convection-diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices.

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References

  1. M. Avellaneda, A. J. Majda: Mathematical models with exact renormalization for turbulent transport. Commun. Math. Phys.131, 381–429 (1990).

    Google Scholar 

  2. M. Avellaneda, A. J. Majda: An Integral Representation and Bounds on the Effective Diffusivity in Passive Advection by Laminar and Turbulent Flows. Commun. Math. Phys.138, 339–391 (1991).

    Google Scholar 

  3. M. Avellaneda, A. J. Majda: Homogenization and renormalization of multiple-scattering expansions of Green functions in turbulent transport. Publications Du Laboratoire D'Analyse Numerique, Universite Pierre et Marie Curie, 1990.

  4. A. Bensoussan, J.L. Lions, G.C. Papanicolaou: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978).

    Google Scholar 

  5. J. Bricmont, A. Kupiainen: Random walks in asymmetric random environments. Commun. Math. Phys.142:2, 345–420 (1991).

    Google Scholar 

  6. A. V. Cherkaev, L. V. Gibiansky: Variational principles for complex conductivity, viscoelasticity, similar problems in media with complex moduli. J. Math. Phys.35:1, 127–145 (1994).

    Google Scholar 

  7. J. L. Doob: Stochastic Processes. John Wiley & Sons, Inc. 1953.

  8. A. Fannjiang: Homogenization and anomalous diffusions in random flows. to appear.

  9. A. Fannjiang, G. C. Papanicolaou: Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math.54, 333–408 (1994)

    Google Scholar 

  10. A. Fannjiang, G. C. Papanicolaou: Convection enhanced diffusion for random flows. to appear.

  11. K. Golden, G. C. Papanicolaou: Bounds for Effective Parameters of heterogeneous Media by Analytic Continuation. Commun. Math. Phys.90, 473–491 (1983).

    Google Scholar 

  12. T. Kato: Perturbation Theory of Linear Operators. Springer Verlag, 1980.

  13. H. Kesten, G. C. Papanicolaou: A limit theorem for turbulent diffusion. Comm. Math. Phys.65, 97–128 (1979)

    Google Scholar 

  14. S. M. Kozlov: The method of averaging and walks in inhomogeneous environments. Russian Math. Surveys40:2, 73–145 (1985).

    Google Scholar 

  15. J. L. Lions: Equations differentielles operationnelles et problems aux limites. Berlin, Springer 1961.

    Google Scholar 

  16. G. Matheron, G. de Marsily: Is transport in porous media always diffusive? A counterexample. Water Resource Res.16, 901–917 (1980).

    Google Scholar 

  17. G.W. Milton: On Characterizing the Set of Possible Effective Tensors of Composites: the Variational Method and the Translational Method. Comm. Pure Appl. Math.43, 63–125 (1990).

    Google Scholar 

  18. K. Oelschlager: Homogenization of a diffusion process in a divergence-free random field. Ann. Prob.16, 1084–1126 (1988).

    Google Scholar 

  19. H. Osada: Homogenization of diffusion processes with random stationary coefficients. Proceeding of the 4-th Japan-USSR Symposium on Probability Theory, Lecture Notes in Math.1021, 507–517, Springer, Berlin, (1982).

    Google Scholar 

  20. G. C. Papanicolaou, S. Varadhan: Boundary value problems with rapidly oscillating random coefficients. (Colloquia Mathematica Societatis Janos Bolyai 27, Random Fields, Esztergom (Hungary) 1979), Amsterdam: North Holland 1982, pp. 835–873.

    Google Scholar 

  21. D. W. Stroock, S. R. S. Varadhan: Multidimensional diffusion processes”. Springer, Berlin Heidelberg New York 1979.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, 95616, Davis, CA, USA

    Albert Fannjiang

  2. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    George Papanicolaou

Authors
  1. Albert Fannjiang
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  2. George Papanicolaou
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Cite this article

Fannjiang, A., Papanicolaou, G. Diffusion in turbulence. Probab. Th. Rel. Fields 105, 279–334 (1996). https://doi.org/10.1007/BF01192211

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  • Received: 03 October 1994

  • Revised: 23 February 1996

  • Issue Date: September 1996

  • DOI: https://doi.org/10.1007/BF01192211

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Mathematics Subject Classification (1991)

  • 60J60
  • 76R50
  • 35R60
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