Effects of the path history on inertial particle pair dynamics in the dissipation range of homogeneous isotropic turbulence

Abstract

The relationship between inertial particle pair dynamics in the dissipation range and local turbulence characteristics is investigated using direct numerical simulations in homogeneous isotropic turbulence at a Reynolds number of 110 based on the Taylor microscale. Seventeen million sub-Kolmogorov-sized particles with Stokes numbers of 0.5, 1.0, 1.5, and 2.0 are tracked backward in time to investigate the formation of the relative velocity of inertial particles in the dissipation range. The numerical experiment shows that particle pairs take different paths and sample different underlying flows depending on the intensity of the local turbulence activity at final locations where the distance between particles is much smaller than the Kolmogorov length scale. Taking different paths depending on the intensity of the local turbulence activity is described by the sling time, which is defined as the time when particle pairs are slung out from the underlying flow. Particle pairs with shorter sling time values than the characteristic time scale of particles are detached from the dissipation range of flow and approach each other in a ballistic fashion. In contrast, the large-scale flow guides particle pairs with longer sling time than the characteristic time scales. In particular, particle pairs forming caustics with the same sling time are detached from similar flows regardless of the magnitude of particle relative velocities. Samplings of similar flows at sling moments cause the scaling relationship between relative velocities of particles and sling time. These behaviors of particle pairs, especially for pairs with caustics in relative velocities, are also observed in the range of considered Stokes numbers. The relationship between the intensity of the local turbulence activity and the paths taken by particles highlights the importance of considering a preferential sampling of flow in understanding inertial particle pair dynamics.