Influence of helicity on the turbulent Prandtl number: Two-loop approximation

Using the field theory renormalization group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent Prandtl number in the model of a scalar field passively advected by the helical turbulent environment given by the stochastic Navier–Stokes equation with a self-similar Gaussian random stirring force $\delta$-correlated in time with the correlator proportional to $k^{4-d-2\varepsilon}$. We briefly discuss the influence of helicity on the stability of the corresponding scaling regime. We show that the presence of helicity increases the value of the turbulent Prandtl number up to 50% of its nonhelical value.