Critical behavior of directed percolation process in the presence of compressible velocity field

Various systems exhibit universal behavior at the critical point. A typical example of the non-equilibrium critical behavior is the directed bond percolation that exhibits an active-to-absorbing state phase transition in the vicinity of critical perco- lation probability. An interesting question is how the turbulent mixing influences its critical behavior. In this work we assume that the turbulent mixing is generated by the compressible Navier-Stokes equation where the compressibility is described by an additional field related to the density. Using field-theoretic models and renormaliza- tion group methods we investigate large scale and long time behavior.