Diffusion Processes in the A-Model of Vector Admixture: Turbulent Prandtl Number

¹ Institute of Experimental Physics, SAS, Košice, Slovakia
² Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russian Federation
³ Dep. of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Košice, Slovakia

^* e-mail: jurcisine@saske.sk
^** e-mail: jurcisin@saske.sk
^*** e-mail: remecky@saske.sk

Published online: 14 February 2018

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 Pr_A,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.