Helical turbulent Prandtl number in the A model of passive advection: Two loop approximation

Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general A model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via continuous parameter ρ ranging from ρ = 0 (no violation of spatial parity) to |ρ| = 1 (maximum violation of spatial parity). Values of A represent a continuously adjustable parameter which governs the interaction structure of the model. In non-helical environments, we demonstrate that A is however restricted to the interval −1.723 ≤ A ≤ 2.800 (rounded on the last presented digit) due to the constraints of two-loop calculations. However, when ρ > 0.749 (rounded on the last presented digit) restrictions may be removed. Furthermore, three physically important cases A ∈ {−1, 0, 1} are shown to lie deep within the allowed interval of A for all values of ρ. For the model of linearized Navier-Stokes equations (A = −1) up to date unknown helical values of turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter A exerts strong influence on advection diffusion processes in turbulent environments with broken spatial parity. In explicit, depending on actual value of A turbulent Prandtl number may increase or decrease with ρ. By varying A continuously we explain high stability of kinematic MHD model (A = 1) against helical effects as a result of its closeness to A = 0.912 (rounded on the last presented digit) case where helical effects are completely suppressed. Contrary, for the physically important A = 0 model we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with |ρ|. We thus identify internal structure of interactions given by parameter A, and not the vector character of the admixture itself to be the dominant factor influencing diffusion advection processes in the helical A model which significantly refines the conclusions of Ref.[1].