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Correlation decay of Lagrangian velocity differences in locally isotropic turbulence

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Zeitschrift für Physik B Condensed Matter

Abstract

The dynamical correlation decay of eddies in fully developed turbulent flows is considered. Eddies of different sizesr are represented by Galilei invariant velocity differences of two fluid elements moving along with the flow, which start a distancer apart. The equal-time statistical properties of the flow are used as partly theoretical, partly experimental input. The method used is the continued fraction representation of the time evolution operator's resolvent. Neglecting memory effects we find the decay rate in the inertial subrange being determined by the ratio of the energy dissipation and the eddy fluctuation strength (represented by the static second order structure function). The decay rate for small eddies,r→0, tends to a Reynolds number dependent constant. The influence of intermittency on the dynamics via statics is evaluated. Inadequate experimental and theoretical information about higher order static structure functions renders an evaluation of the memory contribution impossible. Scaling arguments indicate decreasing relative importance of memory effects in the inertial subrange with increasingr.

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References

  1. Zwanzig, R.: J. Chem. Phys.33, 1338 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  2. Zwanzig, R.: Lectures in theoretical physics. Britten, W.E., Downs, B.W., Downs, J. (eds.), Vol. III, pp. 106–141. New York: Interscience Publishers 1961

    Google Scholar 

  3. Zwanzig, R.: Phys. Rev.124, 983 (1961)

    Article  ADS  MATH  Google Scholar 

  4. Mori, H.: Prog. Theor. Phys.33, 423 (1965)

    Article  ADS  MATH  Google Scholar 

  5. Mori, H.: Prog. Theor. Phys.34, 399 (1965)

    Article  ADS  Google Scholar 

  6. Götze, W., Michel, K.H.: Dynamical Properties of Solids, Horton, G.K., Maradudin, A.A. (eds.), Chap. 9. New York: Elsevier 1974

    Google Scholar 

  7. Bixon, M., Zwanzig, R.: J. Stat. Phys.3, 245 (1971)

    Article  ADS  Google Scholar 

  8. Grossmann, S.: Phys. Rev. A17, 1123 (1978)

    Article  ADS  Google Scholar 

  9. Grossmann, S., Sonneborn-Schmick, B.: Phys. Rev. A25, 2371 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  10. Götze, W., Wölfle, P.: J. Low Temp. Phys.6, 455 (1972)

    Article  ADS  Google Scholar 

  11. Götze, W., Wölfle, P.: Phys. Rev. B6, 1226 (1972)

    Article  ADS  Google Scholar 

  12. Götze, W., Lücke, M.: Phys. Rev. A11, 2173 (1975)

    Article  ADS  Google Scholar 

  13. Götze, W., Zippelius, A.: Phys. Rev. A14, 1842 (1976)

    Article  ADS  Google Scholar 

  14. Götze, W., Lücke, M.: Phys. Rev. B13, 3825 (1976)

    Article  ADS  Google Scholar 

  15. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. 1st ed. London, New York, Paris, Los Angeles: Pergamon 1959

    Google Scholar 

  16. Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics, Vol. I, II. 1st ed. Cambridge, London: MIT Press 1975

    Google Scholar 

  17. Richardson, L.F.: Proc. R. Soc. London Ser. A110, 709 (1926)

    Article  ADS  Google Scholar 

  18. Kolmogorov, A.N.: C.R. Akad. Nauk USSR30, 301 (1941)

    MATH  ADS  Google Scholar 

  19. Batchelor, G.K.: Proc. Camb. Philos. Soc.43, 533 (1947)

    Article  MATH  MathSciNet  Google Scholar 

  20. Robertson, H.P.: Proc. Camb. Philos. Soc.36, 209 (1940)

    MATH  Google Scholar 

  21. Taylor, G.I.: Proc. R. Soc. London, Ser. A151, 421 (1935)

    ADS  MATH  Google Scholar 

  22. Kolmogorov, A.N.: J. Fluid Mech.13, 82 (1962)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. Oboukhov, A.M.: J. Fluid Mech.13, 77 (1962)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Oboukhov, A.M.: J. Geophys. Res.67, 3011 (1962)

    Article  ADS  Google Scholar 

  25. Orszag, S.A.: Phys. Fluids13, 2211 (1970)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Mandelbrot, B.B.: Statistical models and turbulence. Lecture Notes in Physics. Rosenblatt, M., Van Atta, C. (eds.), Vol. 12, pp. 333–351. Berlin, Heidelberg, New York: Springer 1972

    Chapter  Google Scholar 

  27. Mandelbrot, B.B.: J. Fluid Mech.62, 331 (1974)

    Article  ADS  MATH  Google Scholar 

  28. Kuo, A.Y.-Sh., Corrsin, S.: J. Fluid Mech.50, 285 (1971)

    Article  ADS  Google Scholar 

  29. Stewart, R.W., Wilson, J.R., Burling, R.W.: J. Fluid Mech.41, 141 (1970)

    Article  ADS  Google Scholar 

  30. Tennekes, H., Wyngaard, J.C.: J. Fluid Mech.55, 93 (1972)

    Article  ADS  Google Scholar 

  31. Van Atta, C.W., Chen, W.Y.: J. Fluid Mech.44, 145 (1970)

    Article  ADS  Google Scholar 

  32. Van Atta, C.W., Park, J.: Statistical models and turbulence. Lecture Notes in Physics. Rosenblatt, M., Van Atta, C. (eds.), Vol. 12, pp. 402–426. Berlin, Heidelberg, New York: Springer 1972

    Chapter  Google Scholar 

  33. Chen, W.Y.: Phys. Fluids14, 1639 (1971)

    Article  ADS  Google Scholar 

  34. Wyngaard, J.C., Pao, Y.H.: Statistical Models and Turbulence. Lecture Notes in Physics. Rosenblatt, M., Van Atta, C. (eds.), Vol. 12, pp. 384–401. Berlin, Heidelberg, New York: Springer 1972

    Chapter  Google Scholar 

  35. Kolmogorov, A.N.: C.R. Akad. Nauk USSR32, 16 (1941)

    MATH  Google Scholar 

  36. Batchelor, G.K.: Proc. Camb. Philos. Soc.47, 359 (1951)

    MATH  MathSciNet  Google Scholar 

  37. Gibson, C.H., Stegen, G.R., Williams, R.B.: J. Fluid Mech.41, 153 (1970)

    Article  ADS  Google Scholar 

  38. Frisch, U., Sulem, P.-L., Nelkin, M.: J. Fluid Mech.87, 719 (1978)

    Article  ADS  MATH  Google Scholar 

  39. Rose, H.A., Sulem, P.-L.: J. Phys. (Paris)39, 441 (1978)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Fachbereich Physik, Philipps-Universität, Renthof 6, D-3550, Marburg, Federal Republic of Germany

    S. Grossmann & S. Thomae

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  1. S. Grossmann
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  2. S. Thomae
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Grossmann, S., Thomae, S. Correlation decay of Lagrangian velocity differences in locally isotropic turbulence. Z. Physik B - Condensed Matter 49, 253–261 (1982). https://doi.org/10.1007/BF01313034

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  • DOI: https://doi.org/10.1007/BF01313034

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