The influence of helicity on scaling regimes in the extended Kraichnan model

We have investigated the advection of a passive scalar quantity by an incompressible helical turbulent flow in the framework of an extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with zero mean and defined noise with finite time correlation. Actual calculations have been done up to two-loop approximation in the frame of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of a turbulent environment does not affect anomalous scaling which is a peculiar attribute of the corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, strongly depends on the amount of helicity. Moreover, helicity gives rise to the turbulent diffusivity which has been calculated in the one-loop approximation.