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A model of the passive vector field advected by the uncorrelated in timeGaussian velocity with power-like covariance is studied by means of therenormalization group and the operator product expansion. The structurefunctions of the admixture demonstrate essential power-like dependence on theexternal scale in the inertial range (the case of an anomalous scaling). Themethod of finding of independent tensor invariants in the cases of two andthree dimensions is proposed to eliminate linear dependencies between theoperators entering into the operator product expansions of the structurefunctions. The constructed operator bases, which include the powers of thedissipation operator and the enstrophy operator, provide the possibility tocalculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge

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