Geodesic
Influence of finite-time velocity correlations on scaling properties of the magnetic field in the Kazantsev–Kraichnan model: Two-loop renormalization group analysis
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 234-249 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the field theory renormalization group method and the operator product expansion technique in the two-loop approximation, we investigate the influence of the finite-time correlations of a turbulent velocity field on the anomalous scaling behavior of the single-time two-point correlation functions of the passive magnetic field in the framework of the generalized kinematic Kazantsev–Kraichnan model with the presence of large-scale anisotropy in the three-dimensional case. We briefly discuss the scaling regimes of the model and find two-loop expressions for the anomalous dimensions of the leading composite operators in the operator product expansion as explicit functions of the parameter determining the finite-time correlations of the velocity field in the studied model. We show that the anomalous dimensions of the composite operators near the isotropic shell play a central role in the scaling properties of the model and this allows uniquely determining the two-loop expressions for the scaling exponents of all single-time two-point correlation functions of the magnetic field that drive their scaling properties deep inside the inertial interval. We show that the presence of the finite-time correlations of the velocity field leads to a significantly more pronounced anomalous scaling of the magnetic correlation functions compared with the standard Kazantsev–Kraichnan rapid-change model with the $\delta$-time correlated Gaussian velocity field.
Keywords: Kazanstev–Kraichnan model, renormalization group, anomalous scaling.
Mots-clés : turbulence 
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     author = {E. Jur\v{c}i\v{s}inov\'a and M. Jur\v{c}i\v{s}in and M. Menkyna},
     title = {Influence of finite-time velocity correlations on scaling properties of the~magnetic field in {the~Kazantsev{\textendash}Kraichnan} model: {Two-loop} renormalization group analysis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {234--249},
     year = {2019},
     volume = {200},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a4/}
}
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E. Jurčišinová; M. Jurčišin; M. Menkyna. Influence of finite-time velocity correlations on scaling properties of the magnetic field in the Kazantsev–Kraichnan model: Two-loop renormalization group analysis. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 234-249. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a4/

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