title: Turbulent Prandtl number in the A model of passive vector admixture.
abstract: Using the field theoretic renormalization group technique in the second-order (two-loop) approximation the explicit expression for the turbulent vector Prandtl number in the framework of the general A model of passively advected vector field by the turbulent velocity field driven by the stochastic Navier-Stokes equation is found as the function of the spatial dimension d>2. The behavior of the turbulent vector Prandtl number as the function of the spatial dimension d is investigated in detail especially for three physically important special cases, namely, for the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence (A=1), for the passive admixture of a vector impurity by the Navier-Stokes turbulent flow (A=0), and for the model of linearized Navier-Stokes equation (A=-1). It is shown that the turbulent vector Prandtl number in the framework of the A=-1 model is exactly determined already in the one-loop approximation, i.e., that all higher-loop corrections vanish. At the same time, it is shown that it does not depend on spatial dimension d and is equal to 1. On the other hand, it is shown that the turbulent magnetic Prandtl number (A=1) and the turbulent vector Prandtl number in the model of a vector impurity (A=0), which are essentially different at the one-loop level of approximation, become very close to each other when the two-loop corrections are taken into account. It is shown that their relative difference is less than 5% for all integer values of the spatial dimension d≥3. Obtained results demonstrate strong universality of diffusion processes of passively advected scalar and vector quantities in fully symmetric incompressible turbulent environments.
authors.affiliation: Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
authors.forename: E
authors.initials: E
authors.lastname: Jurčišinová
authors.affiliation: Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.|Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovakia.
authors.forename: M
authors.initials: M
authors.lastname: Jurčišin
authors.affiliation: Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.|Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141 980 Dubna, Moscow Region, Russian Federation.
authors.forename: R
authors.initials: R
authors.lastname: Remecký