  The direct bond percolation process (Gribov process) is studied in the
presence of random velocity fluctuations generated by the Gaussian self-similar
ensemble with finite correlation time. We employ the renormalization group in
order to analyze a combined effect of the compressibility and finite
correlation time on the long-time behavior of the phase transition between an
active and an absorbing state. The renormalization procedure is performed to
the one-loop order. Stable fixed points of the renormalization group and their
regions of stability are calculated in the one-loop approximation within the
three-parameter $(\eps,y,\eta)$-expansion. Different regimes corresponding to
the rapid-change limit and frozen velocity field are discussed, and their fixed
points' structure is determined in numerical fashion.
