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

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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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     author = {L. Ts. Adzhemyan and S. V. Novikov},
     title = {Anomalous scaling in the model of turbulent advection of a vector field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {467--487},
     publisher = {mathdoc},
     volume = {146},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a8/}
}
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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/