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 TMF, 2006, Volume 146, Number 3, Pages 467–487 (Mi tmf2048)

Anomalous scaling in the model of turbulent advection of a vector field

L. Ts. Adzhemyan, S. V. Novikov

Saint-Petersburg State University

Abstract: We consider the model of turbulent advection of a passive vector field $\varphi$ by a two-dimensional random velocity field uncorrelated in time and having Gaussian statistics with a powerlike correlator. The renormalization group and operator product expansion methods show that the asymptotic form of the structure functions of the $\varphi$ field in the inertial range is determined by the fluctuations of the energy dissipation rate. The dependence of the asymptotic form on the external turbulence scale is essential and has a powerlike form (anomalous scaling). The corresponding exponents are determined by the spectrum of the anomalous dimension matrices of operator families consisting of gradients of $\varphi$. We find a basis constructed from powers of the dissipation and enstrophy operators in which these matrices have a triangular form in all orders of the perturbation theory. In the two-loop approximation, we evaluate the anomalous-scaling exponents for the structure functions of an arbitrary order.

Keywords: turbulence, passive admixture, anomalous scaling, renormalization group

DOI: https://doi.org/10.4213/tmf2048

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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 393–410

Bibliographic databases:

Citation: L. Ts. Adzhemyan, S. V. Novikov, “Anomalous scaling in the model of turbulent advection of a vector field”, TMF, 146:3 (2006), 467–487; Theoret. and Math. Phys., 146:3 (2006), 393–410

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf2048
• https://doi.org/10.4213/tmf2048
• http://mi.mathnet.ru/eng/tmf/v146/i3/p467

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Antonov, NV, “Renormalization group, operator product expansion and anomalous scaling in models of turbulent advection”, Journal of Physics A-Mathematical and General, 39:25 (2006), 7825
2. Jurcisinova E., Jurcisin M., Remecky R., “Turbulent Prandtl Number in a Model of Passively Advected Vector Field: Two-Loop Renormalization Group Result”, Phys. Rev. E, 88:1 (2013), 011002
3. Jurcisinova E., Jurcisin M., Zalom P., “Turbulent Prandtl Number of a Passively Advected Vector Field in Helical Environment: Two-Loop Renormalization Group Result”, Phys. Rev. E, 89:4 (2014), 043023
4. Jurcisinova E. Jurcisin M. Remecky R., Phys. Rev. E, 93:3 (2016), 033106
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