  We have investigated the advection of a passive scalar quantity by
incompressible helical turbulent flow in the frame of 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 turbulent environment does not affect anomalous scaling
which is peculiar attribute of 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 one-loop approximation.
