The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and
isotropic turbulence is studied by means of direct numerical simulations at two values of
the Taylor-scale Reynolds number Re¿ ~ 200 and Re¿ ~ 400, corresponding to resolutions
of 512 3 and 2048 3 grid points, respectively. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle
density ratio. For particles much heavier than the fluid, the range of available Stokes
numbers is St ¿ [0.1 : 70], while for light particles the Stokes numbers span the range
St ¿ [0.1:3] and the density ratio is varied up to the limit of vanishing particle density.
For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a
second regime starts where heavy particles separate as tracers particles would do. As a
consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed, and which is supported by the numerical results. In the case of light particles with high density ratios, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation
increases with time. This effect strongly alters the shape of the probability density function of light particle separations.
|Number of pages||28|
|Publication status||Published - 2009|