Noise- and inertia-induced inhomogeneity in the distribution of small particles in fluid flows

The dynamics of small spherical neutrally buoyant particulate impuritiesimmersed in a two-dimensional fluid flow are known to lead to particleaccumulation in the regions of the flow in which rotation dominates over shear,provided that the Stokes number of the particles is sufficiently small. If theflow is viewed as a Hamiltonian dynamical system, it can be seen that theaccumulations occur in the nonchaotic parts of the phase space: theKolmogorov--Arnold--Moser tori. This has suggested a generalization of thesedynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we usea bailout embedding of the standard map to mimic the dynamics of impuritiessubject not only to drag but also to fluctuating forces modelled as whitenoise. We find that the generation of inhomogeneities associated with theseparation of particle from fluid trajectories is enhanced by the presence ofnoise, so that they appear in much broader ranges of the Stokes number thanthose allowing spontaneous separation.