Statistical theory of the diffusion of a passive tracer in a random velocity field

A passive tracer on the surface of an incompressible liquid behaves like a tracer in two-dimensional compressible flows, whose characteristic feature is the formation of cluster structures, i.e., compact regions of increased density surrounded by vast low-density regions. The cluster formation dynamics are studied, and statistical spatiotemporal characteristics of the density fields, which faithfully reflect the properties of the cluster structures, are calculated.