Using the field theoretic renormalization group technique the simultaneous influence of the compressibility and finite time correlations of the non-solenoidal Gaussian velocity field on the advection of a passive scalar field is studied within the generalized Kraichnan model in three spatial dimensions up to the second-order approximation in the corresponding perturbative expansion. All possible infrared stable fixed points of the model, which drive the corresponding scaling regimes of the model, are identified and their regions of the infrared stability in the model parametric space are discussed. It is shown that, depending on the value of the parameter that drives the compressibility of the system, there exists a gap in the parametric space between the regions where the model with the frozen velocity field and the model with finite-time correlations of the velocity field are stable or there exists an overlap between them.
On the effect of finite-time correlations on the turbulent mixing in smooth chaotic compressible velocity fields
