Divergence and convergence of inertial particles in high-Reynolds-number turbulence

Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analysed using Voronoi tessellation of the particle positions and considering different Stokes numbers. A finite-time measure to quantify the divergence of the particle velocity by determining the volume change rate of the Voronoi cells is proposed. For inertial particles, the probability distribution function of the divergence deviates from that for fluid particles. Joint probability distribution functions of the divergence and the Voronoi volume illustrate that the divergence is most prominent in cluster regions and less pronounced in void regions. For larger volumes, the results show negative divergence values which represent cluster formation (i.e. particle convergence) and, for small volumes, the results show positive divergence values which represents cluster destruction/void formation (i.e. particle divergence). Moreover, when the Stokes number increases the divergence takes larger values, which gives some evidence why fine clusters are less observed for large Stokes numbers.