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Two-parameter expansion in the renormalization-group analysis of turbulence

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Zeitschrift für Physik B Condensed Matter

Abstract

The renormalization of the solution of the Navier-Stokes equation for randomly stirred fluid with long-range correlations of the driving force is analysed near two dimensions. It is shown that a local term must be added to the correlation function of the random force for the correct renormalization of the model at two dimensions. The interplay of the short-range and long-range terms in the large-scale behaviour of the model is analysed near two dimensions by the field-theoretic renormalization group. A regular expansion in 2ε=d-2 and δ=2-λ is constructed, whered is the space dimension and λ the exponent of the powerlike correlation function of the driving force. It is shown that in spite of the additional divergences, the asymptotic behaviour of the model near two dimensions is the same as in higher dimensions, contrary to recent conjectures based on an incorrect renormalization procedure.

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References

  1. Forster, D., Nelson, D.R., Stephen, M.J.: Phys. Rev. A16, 732 (1977)

    Article  Google Scholar 

  2. De Dominicis, C., Martin, P.C.: Phys. Rev. A29, 419 (1979) Adzhemyan, L.Ts., Pis'mak, Yu.M., Vasil'ev, A.N.: Teor. Mat. Fiz.57, 268 (1983)

    Article  Google Scholar 

  3. Yachot, V., Orszag, S.A.: Phys. Rev. Lett.57, 1722 (1986); J. Sci. Comp.1, 3 (1986)

    Article  Google Scholar 

  4. Wyld, H.W.: Ann. Phys.14, 143 (1961)

    Article  Google Scholar 

  5. Amit, D.J.: Field theory, the renormalization group and critical phenomena. London: McGraw-Hill 1978

    Google Scholar 

  6. Monin, A.S., Yaglom, A.M.: Statistical fluid mechanics: mechanics of turbulence, vol 2. Cambridge: MIT Press 1975

    Google Scholar 

  7. Ronis, D.: Phys. Rev. A36, 3322 (1987)

    Article  CAS  Google Scholar 

  8. Fournier, J.-D., Sulem, P.-L., Pouquet, A.: J. Phys. A.: Math. Gen.15, 1393 (1982); Adzhemyan, L.Tŝ., Vasil'ev, A.N., Hnatic, M.: Teor. Mat. Fiz.64, 196 (1985)

    Article  Google Scholar 

  9. Olla, P.: Phys. Rev. Lett.67, 2465 (1991); Int. J. Mod. Phys. B8, 581 (1994)

    Article  CAS  Google Scholar 

  10. Collins, J.: Renormalization. Cambridge: Cambridge University Press 1985.

    Google Scholar 

  11. Honkonen, J., Nalimov, M.Yu.: J. Phys. A: Math. Gen.22, 751 (1989)

    Article  Google Scholar 

  12. Adzhemyan, L.Ts., Vasil'ev, A.N., Hnatic, M.: Teor. Mat. Fiz.74, 180 (1988)

    CAS  Google Scholar 

  13. Adzhemyan, L.Ts., Nalimov, M.Yu.: Teor. Mat. Fiz.91, 294 (1992)

    Article  CAS  Google Scholar 

  14. Antonia, R.A., Hopfinger, E.J., Gagne, Y., Anselmet, F.: Phys. Rev. A30, 2704 (1984)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Theory Division, University of Helsinki, (Siltavuorenpenger 20 C), P.O. Box 9, FIN-00014, Finland

    J. Honkonen

  2. Department of Theoretical Physics, State University of St. Petersburg, Ul'yanovskaya 1, 198904 Staryi Petergof, St. Petersburg, Russia

    M. Yu. Nalimov

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  1. J. Honkonen
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  2. M. Yu. Nalimov
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Correspondence to J. Honkonen.

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Honkonen, J., Nalimov, M.Y. Two-parameter expansion in the renormalization-group analysis of turbulence. Z. Phys. B - Condensed Matter 99, 297–303 (1995). https://doi.org/10.1007/BF02769945

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  • DOI: https://doi.org/10.1007/BF02769945

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