Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow

Abstract

A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the admixture demonstrate essential power-like dependence on the external scale in the inertial range (the case of an anomalous scaling). The method of finding of independent tensor invariants in the cases of two and three dimensions is proposed to eliminate linear dependencies between the operators entering into the operator product expansions of the structure functions. The constructed operator bases, which include the powers of the dissipation operator and the enstrophy operator, provide the possibility to calculate the exponents of the anomalous scaling.

9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Gen

References in corpus (13)

• ANOMALOUS SCALING OF THE PASSIVE SCALAR
• Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
• Anomalous Scaling Exponents of a White-Advected Passive Scalar
• Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar
• Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
• Anomalous Scaling in the N-Point Functions of Passive Scalar
• Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
• Symmetry and Scaling of Turbulent Mixing
• Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
• Anomalous exponents in the rapid-change model of the passive scalar advection in the order ${\epsilon }^3$
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
• Spectrum of Anisotropic Exponents in Hydrodynamic Systems with Pressure

Cited by in corpus (3)

• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation