Dispersion of mass by two-dimensional homogeneous and incompressible Cinlar flows

Abstract

We consider the dispersion of passive tracers in stationary, homogeneous and incompressible Cinlar flows on the plane. The associated velocity field is generated by the superposition of eddies of various size, arrival time and location which form a Poisson point process. Our focus is on the dispersion of a tracer cloud, which is measured through the variance of its centroid and the mean of the dispersion tensor. We also study single particle dispersion and particle pair separations in conjunction with dispersion. Monte Carlo simulations of all these measures first establish the relation of the dispersion to the parameters of the flow model. Second, the physical predictions on the behavior of these measures with respect to time as well as their relationship to each other are confirmed.