Pair dispersion of inertial particles crossing stably stratified turbulent/non-turbulent interfaces

Abstract

In the present work we study the pair dispersion of inertial particles crossing two-layer stably stratified turbulent/non-turbulent interfaces (STNTI) of finite thickness. The goal is to investigate two-particle dispersion, a problem of great importance in a wide range of applications, within very complex flows. STNTI flows are in fact constituted not only by non-homogeneous turbulence and density stratification, but also by effects generated by their interaction, such as internal waves. The problem is addressed numerically, two direct numerical simulations (DNS) of STNTI flow are performed: moderate intensity turbulence, Reλ=35,44 is produced in the DNSs using a convective forcing (heat source at the domain boundary) in one case, and a forcing that mimics a vertically oscillating grid, through an immersed boundary method, in the other. We tracked inertial particles, with one-way coupling approach, using a modified Basset-Boussinesq-Oseen equation which includes a stratification-induced term FS. We first analyze particle pairs settling from the turbulent region toward the STNTI and then pairs moving in the opposite direction from the non-turbulent layer. In general results for all pair tested present a t2-scaling law for small times. Pairs crossing the STNTI from the non-turbulent region show a peculiar dispersion behavior: approaching the internal waves layer, pairs tend to reduce the dispersion rate and then they present a fast growing separation regime (tα, α≥6) possibly induced by non-local effects. Different particle densities, which affect inertia, the initial pair separation and the effect of stratification on the dispersion, by means of FS, are tested as well. Results confirm the importance of the first two parameters for the pair evolution. The stratification force, which has been not taken into account so far, plays as well an important role, which may lead to discrepancies in pair dispersion larger than the role FS has in the equation of motion itself.