Diffusion and Clustering of Passive Intermixture in Random Hydrodynamic Flows

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The book, based on a functional approach with a single point of view, we consider problems of the diffusion of a passive tracer in random flows in Lagrangian and in Eulerian representation. The main attention is focused on the description of coherent phenomena based on the ideas of statistical topography. These phenomena are occurring with a probability equal to unity, there are almost all implementations of impurity diffusion. These include such things as the clustering of particles and tracer field in random compressible velocity fields with a potential component, low-inertia particles clustering in random incompressible velocity fields, a sharp aggravation of the field gradients of density and appearance of the fractal structure contours of constant concentration in the divergence-free velocity fields. All these phenomena are studied based on a single approach based on the analysis of one-point space-time probability densities.