Abstract: I will discuss the problem of homogenization for the Cauchy problem for a semilinear advection equation, where the drift coefficient is given by an Ornstein-Uhlenbeck type stationary in time and space random field with incompressible realizations and the non-linearity is given by another random stationary field. We show the existence of the limit of solutions under the diffusive time-space scaling. Our main tool is the method of characteristics used to represent the solution of the equation. This is a joint work with L. Ryzhik (Stanford Univ.) and Yu Gu (Carnegie Mellon Univ.)