Percolation process in the presence of velocity fluctuations: two-loop approximation

Abstract

Critical behaviour of directed bond percolation is studied in presence of turbulent mixing. The turbulent advecting velocity field is assumed to be incompressible and generated by the Kraichnan model. The model is studied by means of field-theoretic approach. The renormalization group (RG) method is used in order to analyze asymptotic large-scale behavior of the model near its critical point. The renormalization procedure is performed to the next-to-leading order of the perturbation theory. Partial results of full two-loop calculation are given.