Anomalous scaling in helical turbulent environment

The influence of helicity on the anomalous scaling of the single-time structure functions of a passive scalar advected by a non-Gaussian velocity field driven by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and the operator-product expansion within the second order of the perturbation theory (two-loop approximation). The set of compositeoperators with the minimal critical dimensions is identified and their dependence on the helicity parameter is found. It is shown that the contribution to the critical dimensions of the structure functions of a passive scalar is given only by parts of the composite operators which are independent of the helicity parameter. Therefore, it is shown that the spatial parity violation has no impact on the anomalous scaling behavior of the passively advected scalar quantity in the turbulent environment.