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The direct bond percolation process (Gribov process) is studied in thepresence of irrotational velocity fluctuations with long-range correlations.The perturbative renormalization group is employed in order to analyze theeffects of finite correlation time on the long-time behavior of the phasetransition between an active and an ab- sorbing state. The calculation isperformed to the one-loop order. Stable fixed points of the renormalizationgroup and their regions of stability are obtained within the three-parameter$(\epsilon,y,\eta)$- expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed.

Gribov process advected by the synthetic compressible velocity ensemble: Renormalization Group Approach