Passive Advection of Particles Denser than the Surrounding Fluid

We study the diffusion of passive test particles convected by a two-dimensional, non-divergent steady velocity field with stream function ψ = 2(cosx + cosy). The particle motions depend strongly on the ratio δ between the fluid and the particle density. Advected particles which are lighter than the fluid converge to the centers of the convection cells where the velocity field is zero. On the opposite, the motions of advected particles which are denser than the surrounding fluid are not bounded in single convection cells; in this case the particles wander throughout the whole space. For small values of ϵ = 1 − δ, the particle motion is characterized by well-defined diffusion coefficients Dx and Dy. Numerical analysis of the behaviour of Dx and Dy as functions of ϵ reveals a scaling behavior which is similar to that observed for the transport of fluid particles in a steady, periodic two-dimensional flow perturbed by an additive white noise component. In our case the role of bare diffusion coefficient is played by ϵ.