Turbulent Prandtl number of a passively advected vector field in helical environment: two-loop renormalization group result.

Abstract

Using the field-theoretic renormalization group technique in the two-loop approximation, the influence of helicity (spatial parity violation) on the turbulent vector Prandtl number is investigated in the model of a passive vector field advected by the turbulent helical environment driven by the stochastic Navier-Stokes equation. It is shown that the presence of helicity in the turbulent environment can significantly decrease the value of the turbulent vector Prandtl number by up to 15% of its nonhelical value. This result is compared to the corresponding results obtained recently for the turbulent Prandtl number of a passively advected scalar quantity as well as for the turbulent magnetic Prandtl number of a weak magnetic field in the framework of the kinematic magnetohydrodynamic turbulence. It is shown that the behavior of the turbulent vector Prandtl number as function of the helicity parameter is much closer to the corresponding behavior of the turbulent Prandtl number of the scalar quantity than to the behavior of the turbulent magnetic Prandtl number.