Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: two-loop approximation.

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator-product expansion within the two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents epsilon-eta, where epsilon characterizes the energy spectrum of the velocity field in the inertial range E proportional to k(1-2epsilon), and eta is related to the correlation time at the wave number k, which is scaled as k(-2+eta). The restrictions given by nonzero helicity on the regions with stable fixed points that correspond to the scaling regimes are analyzed in detail.