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We derive a perturbative approach to study, in the large inertia limit, thedynamics of solid particles in a smooth, incompressible and finite-timecorrelated random velocity field. We carry on an expansion in powers of theinverse square root of the Stokes number, defined as the ratio of therelaxation time for the particle velocities and the correlation time of thevelocity field. We describe in this limit the residual concentrationfluctuations of the particle suspension, and determine the contribution to thecollision statistics produced by clustering. For both concentrationfluctuations and collision velocities, we analyze the differences with thecompressible one-dimensional case.

Perturbation theory for large Stokes number particles in random velocity fields