Title: Toy models of developed turbulence
Authors: M.Hnatich, M.Jurcisin, M.Repasan (Institute of Experimental Physics, Dept. Theor.Phys., Kosice, Watsonova 47, Slovakia)

We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow within the framework 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 within the framework of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of 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 one-loop approximation.

Key words: helicity, diffusivity, anomalous scaling, renormalization group
PACS: 47.10.+g, 47.27.-i, 05.10.Cc