Influence of weak anisotropy on scaling regimes in a model of advected vector field

Influence of weak uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Weak anisotropy means that parameters which describe anisotropy are chosen to be close to zero, therefore in all expressions it is enough to leave only linear terms in anisotropy parameters. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy but the corresponding stability of the two-dimensional system can be destroyed even by the presence of weak anisotropy. A borderline dimension $d_c$ below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters.