Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field.

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. The amplitude of the concentration fluctuations is characterized by slow decay at large inertia and a much larger correlation length than that of the random field. The fluctuation structure in velocity space is very different from predictions from short-time correlated random velocity fields, with only few particle pairs crossing at sufficiently small relative velocity to produce correlations. Concentration fluctuations are associated with depletion of the relative velocity variance of colliding particles.