TY - JOUR

T1 - Anomalous scaling in statistical models of passively advected vector fields

AU - Antonov, N.V.

AU - Gulitskiy, N.M.

PY - 2013

Y1 - 2013

N2 - The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of passively advected vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The advecting turbulent velocity field is governed by the stochastic Navier--Stokes equation. It is shown that the correlation functions of the passive vector field in the inertial range exhibit anomalous scaling behaviour. The corresponding anomalous exponents are determined by the critical dimensions of tensor composite fields (operators) built solely of the passive vector field. They are calculated (including the anisotropic sectors) in the leading order of the expansion in $y$, the exponent entering the correlator of the stirring force in the Navier--Stokes equation (one-loop approximation of the renormalization group). The anomalous exponents exhibit an hierarchy related to the degree of anisotropy: the less is the rank of the tensor operator, the less is its dimension. Thus th

AB - The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of passively advected vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The advecting turbulent velocity field is governed by the stochastic Navier--Stokes equation. It is shown that the correlation functions of the passive vector field in the inertial range exhibit anomalous scaling behaviour. The corresponding anomalous exponents are determined by the critical dimensions of tensor composite fields (operators) built solely of the passive vector field. They are calculated (including the anisotropic sectors) in the leading order of the expansion in $y$, the exponent entering the correlator of the stirring force in the Navier--Stokes equation (one-loop approximation of the renormalization group). The anomalous exponents exhibit an hierarchy related to the degree of anisotropy: the less is the rank of the tensor operator, the less is its dimension. Thus th

KW - passive vector field

KW - turbulent advection

KW - anomalous scaling

KW - renormalization group

KW - operator product expansion

U2 - 10.1007/s11232-013-0072-7

DO - 10.1007/s11232-013-0072-7

M3 - Article

VL - 176

SP - 851

EP - 860

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -