Combine effects of compressibility and helicity on the scaling regimes of a passive scalar advected by turbulent velocity field with finite correlation time

The influence of compressibility and helicity on the stability of the scaling regimes of a passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop approximation. The influence of helicity and compressibility on the scaling regimes is discussed as a function of the exponents ε and η, where ε characterizes the energy spectrum of the velocity field in the inertial range E ∝ k, and η is related to the correlation time at the wave number k which is scaled as k. The restrictions given by nonzero compressibility and helicity on the regions with stable infrared fixed points which correspond to the stable infrared scaling regimes are discussed. A special attention is paid to the case of so-called frozen velocity field when the velocity correlator is time independent. In this case, explicit inequalities which must be fulfilled in the plane ε− η are determined within two-loop approximation.