Monte Carlo Studies of Effective Diffusivities for Inertial Particles

The transport of inertial particles in incompressible flows and subject to molecular diffusion is studied through direct numerical simulations. It was shown in recent work [9, 15] that the long time behavior of inertial particles, with motion governed by Stokes' law in a periodic velocity field and in the presence of molecular diffusion, is diffusive. The effective diffusivity is defined through the solution of a degenerate elliptic partial differential equation. In this paper we study the dependence of the effective diffusivity on the non-dimensional parameters of the problem, as well as on the streamline topology, for a class of two dimensional periodic incompressible flows.