Stochastic transport of passive tracer by random flows

This review paper gives a unified functional approach to problems of the tu rbulent diffusion of a passive tracer in random flows, for both the Euleria n and the Lagrangian description. The discussion is based on the ideas of s tatistical topography. We focus on coherent phenomena, which take place wit h probability one, i.e., for almost all realizations of the diffusion proce ss. They include clustering of tracer particles and densities in random com pressible velocity fields, as well as sharpening of gradients and fractaliz ation of the density isolines in incompressible flows. All these phenomena are studied using a unified method based on the analysis of the one-point s pace-time probability density functions. We compute the basic parameters th at characterize these phenomena. Our analysis is based on the Gaussian delt a-correlated velocity fluctuations.