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

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Abstract

We consider the model of turbulent advection of a passive vector field ϕ 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 ϕ 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 ϕ. 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.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 467–487, March, 2006.

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Adzhemyan, L.T., Novikov, S.V. Anomalous scaling in the model of turbulent advection of a vector field. Theor Math Phys 146, 393–410 (2006). https://doi.org/10.1007/s11232-006-0048-y

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Keywords

  • turbulence
  • passive admixture
  • anomalous scaling
  • renormalization group