Geodesic
Anomalous scaling in the model of turbulent advection of a vector field
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 467-487 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : turbulence, passive admixture
Keywords: anomalous scaling, renormalization group. 
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L. Ts. Adzhemyan; S. V. Novikov. Anomalous scaling in the model of turbulent advection of a vector field. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 467-487. http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a8/

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