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Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator

  • Statistical and Nonlinear Physics
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Abstract

A method is put forward to improve the ε expansion in the theory of developed d-dimensional turbulence on the basis of the renormalization of random forcing in the stochastic Navier-Stokes equation. This renormalization takes into account additional divergences, which appear as d →2. In the nth order of the perturbation theory with the extended renormalization the first n terms of the usual ε expansion are correctly reproduced as well as the first n terms of the Laurent expansion in the parameter d-2 of the terms of the rest of the usual ε expansion. The Kolmogorov constant and skewness factor calculated in the one-loop approximation of the improved perturbation theory are in reasonable agreement with their recommended experimental values.

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References

  1. K.G. Wilson, J. Kogut, Phys. Rep. 12, 75 (1974)

    Article  ADS  Google Scholar 

  2. C. De Dominicis, P.C. Martin, Phys. Rev. A 19, 419 (1979)

    Article  ADS  Google Scholar 

  3. L.T. Adzhemyan, A.N. Vasil’ev, Yu. M. Pis’mak, Teor. Mat. Fiz. 57, 268 (1983)

    MATH  MathSciNet  Google Scholar 

  4. L.T. Adzhemyan, N.V. Antonov, A.N. Vasil’ev, Usp. Fiz. Nauk 166, 1257 (1996) [Phys. Usp. 39, 1193 (1996)]

    Article  Google Scholar 

  5. L.T. Adzhemyan, N.V. Antonov, A.N. Vasiliev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon & Breach, London, 1999)

    MATH  Google Scholar 

  6. L.T. Adzhemyan, N.V. Antonov, M.V. Kompaniets, A.N. Vasil’ev, Int. J. Mod. Phys. B 17, 2137 (2003)

    Article  MATH  ADS  Google Scholar 

  7. L.T. Adzhemyan, J. Honkonen, M.V. Kompaniets, A.N. Vasil’ev, Phys. Rev. E 68, R055302 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  8. L.T. Adzhemyan, J. Honkonen, M.V. Kompaniets, A.N. Vasil’ev, Phys. Rev. E 71, 036305 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  9. D. Ronis, Phys. Rev. A 36, 3322 (1987)

    Article  ADS  Google Scholar 

  10. J. Honkonen, M.Yu. Nalimov, Z. Phys. B 99, 297 (1996)

    Article  ADS  Google Scholar 

  11. W.D. McComb, The Physics of Fluid Turbulence (Clarendon Press, Oxford, 1992)

    Google Scholar 

  12. G.I. Barenblatt, A.J. Chorin, V.M. Prostokishin, Physica D 127, 105 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. R. Benzi, S. Ciliberto, C. Baudet, G. Ruiz-Chavarria, Physica D 127, 111 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, 1975), Vol.2

    Google Scholar 

  15. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995)

    MATH  Google Scholar 

  16. L.T. Adzhemyan, N.V. Antonov, M.V. Kompaniets, A.N. Vasil’ev, Acta Physica Slovaca 52, 565 (2002)

    Google Scholar 

  17. K.R. Sreenivasan, Phys. Fluids 7, 2778 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. A. Pelissetto, E. Vicari, Phys. Rep. 368, 549 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Theoretical Physics, St. Petersburg University, Ulyanovskaya 1, St. Petersburg, Petrodvorets, 198504, Russia

    L. T. Adzhemyan

  2. Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01, Košice, Slovakia

    M. Hnatich

  3. Faculty of Sciences, P.J. Šafarik University, Moyzesova 16, 040 01, Košice, Slovakia

    M. Hnatich

  4. Department of Military Technology, National Defence University, P.O. Box 7, Helsinki, Finland

    J. Honkonen

Authors
  1. L. T. Adzhemyan
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  2. M. Hnatich
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  3. J. Honkonen
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Correspondence to J. Honkonen.

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Adzhemyan, L., Hnatich, M. & Honkonen, J. Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator. Eur. Phys. J. B 73, 275–285 (2010). https://doi.org/10.1140/epjb/e2009-00432-8

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  • DOI: https://doi.org/10.1140/epjb/e2009-00432-8

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