Two-parameter expansion in the renormalization-group analysis of turbulence |
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Authors: | J Honkonen M Yu Nalimov |
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Institution: | (1) Department of Physics, Theory Division, University of Helsinki, (Siltavuorenpenger 20 C), P.O. Box 9, FIN-00014, Finland;(2) Department of Theoretical Physics, State University of St. Petersburg, Ul'yanovskaya 1, 198904 Staryi Petergof, St. Petersburg, Russia |
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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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Keywords: | 05 40 +j 11 10 Hi 47 27 Gs |
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