Abstract
Using analytical approach of the field theoretic renormalization-group technique in two-loop approximation we model a fully developed turbulent system with vector characteristics driven by stochastic Navier-Stokes equation. The behaviour of the turbulent Prandtl number PrA,t is investigated as a function of parameter A and spatial dimension d > 2 for three cases, namely, kinematic MHD turbulence (A = 1), the admixture of a vector impurity by the Navier-Stokes turbulent flow (A = 0) and the model of linearized Navier-Stokes equation (A = −1). It is shown that for A = −1 the turbulent Prandtl number is given already in the one-loop approximation and does not depend on d while turbulent Prandt numbers in first two cases show very similar behaviour as functions of dimension d in the two-loop approximation.
Highlights
The problems related to the behavior of various admixtures in turbulent environments are among the most studied in the framework of the turbulent fluid dynamics
During the last few decades various field theoretical models of passive advection were developed for the analysis of the intermittency and anomalous scaling behavior of various correlation functions, for the investigation of deviations from the simple scaling predictions of the classical phenomenological Kolmogorov-Obukhov theory [6]
In the present paper we investigate the turbulent vector Prandtl number in the framework of the general A model [7,8,9,10] of a passive vector quantity advected by the turbulent velocity field driven by the stochastic Navier-Stokes equation
Summary
The problems related to the behavior of various admixtures in turbulent environments are among the most studied in the framework of the turbulent fluid dynamics. In the present paper we investigate the turbulent vector Prandtl number in the framework of the general A model [7,8,9,10] of a passive vector quantity advected by the turbulent velocity field driven by the stochastic Navier-Stokes equation This model describes three physically important cases of passive vector admixture, namely, the passive advection of the magnetic field in a conductive turbulent environment in the framework of the kinematic MHD turbulence with A = 1 [8, 11, 12], the passive admixture of a vector impurity by the Navier-Stokes turbulent flow with A = 0 [13, 14], and the model of linearized Navier-Stokes equation with A = −1
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