The dispersion of fluid particles in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. Due to anisotropy of the flow, horizontal and vertical dispersion show different behavior. Single-particle dispersion in horizontal direction is similar to that in isotropic turbulence for short times, but shows a long-time growth rate proportional to t2.1±0.1, larger than the classical linear diffusion limit. In vertical direction, three successive regimes can be identified: a classical t2-regime, a plateau that scales as N−2, and a diffusion limit where dispersion is proportional to t. By forcing the flow and performing long-time simulations, we are able to observe this last regime, which was predicted but not observed before in stratified turbulence. This diffusive regime is caused by molecular diffusion of the active scalar (density). The mean squared separation of particle pairs (relative dispersion) in vertical direction shows two plateaus that are not present in isotropic turbulence. They can be associated with the characteristic layered structure of the flow. In the long-time limit again a linear regime is found as for single-particle dispersion. Pair dispersion in horizontal direction behaves similar to that in isotropic turbulence except for long times. Finally, the study of multiparticle statistics in stably stratified turbulent flows is reported. The evolution of tetrads gives an impression of the shape of particle clouds. It is found that with increasing stratification, the volume of the tetrads decreases, and they become flatter and more elongated.

The dispersion of light inertial particles ͓ p / f = O͑1͔͒ in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. The light particle dispersion behavior is found to be comparable to that of heavy particles when displayed as a function of the Stokes number. Deviations from fluid particle dispersion are found already for small Stokes numbers; the length of the typical plateau for vertical dispersion is shorter for the light inertial particles. All the forces in the Maxey-Riley equation are taken into account and they are found to be of similar magnitude as the Stokes drag for particles with p / f = O͑1͒. However, not all forces directly influence the particle dispersion. It is shown that especially the often neglected Basset force plays a considerable role in the vertical dispersion of light particles in stratified turbulence. Neglecting this force results in an overprediction of the vertical dispersion by about 15%-20%.

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The dispersion of heavy inertial particles in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. The following issues have been addressed: What distinguishes dispersion in such stratified flows from dispersion processes in statistically stationary homogeneous isotropic turbulence? How is the dispersion process affected by the Stokes number of the inertial particles ͑0.1Շ St= p / K Շ 10, with p the particle response time and K the Kolmogorov time͒? What is the interplay between buoyancy and the Stokes number? And what is the effect, if any, of particle settling, nonlinear drag, and lift forces ͑particularly relevant for stratified turbulence with its vertical shear layers͒ on particle dispersion? The long-time dispersion in isotropic turbulence is found to be maximum around St= 1, in agreement with the observation of preferential concentration for StϷ 1. In stably stratified turbulence such a maximum in the dispersion is only found for the horizontal direction. The horizontal and vertical dispersions in stably stratified turbulence show different behaviors due to the anisotropy of the flow, and in particular, vertical dispersion is strongly affected by the inertia of the particles. With increasing St the classical plateau found for vertical fluid particle dispersion becomes less pronounced and it even vanishes for Stokes numbers of O͑10͒ and higher. Furthermore, the long-time vertical dispersion increases with increasing St. The effects of gravity, nonlinear drag, and lift forces have been considered in more detail. It turned out that the settling enhancement of inertial particles, as observed in isotropic turbulence, is suppressed by stratification and by nonlinear drag effects. Moreover, nonlinear drag only affects the dispersion in the vertical direction in stably stratified turbulence. Finally, it is found that lift forces can safely be neglected for dispersion studies under the current parameter settings.

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