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Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.
MedLine Citation:
PMID:  15697718     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.
Authors:
L Ts Adzhemyan; N V Antonov; J Honkonen; T L Kim
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Publication Detail:
Type:  Journal Article     Date:  2005-01-07
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  71     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2005 Jan 
Date Detail:
Created Date:  2005-02-08     Completed Date:  2005-05-19     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  016303     Citation Subset:  -    
Affiliation:
Department of Theoretical Physics, St. Petersburg University, Uljanovskaya 1, St. Petersburg-Petrodvorez, 198504, Russia.
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