Quantitative prediction of sling events in turbulence at high Reynolds numbers

TL;DR

This paper develops a quantitative criterion for sling events in turbulent flows, linking particle collision dynamics to velocity gradient eigenvalues, validated through simulations and applicable to cloud physics.

Contribution

It introduces a new criterion based on velocity gradient eigenvalues for predicting sling events, supported by theory and turbulence simulations.

Findings

Sling events are controlled by the smallest negative eigenvalue of the velocity gradient tensor.

Predictions are confirmed by fully resolved turbulence simulations.

Sling events at high Reynolds numbers are significantly enhanced for small Stokes numbers.

Abstract

Collisional growth of droplets, such as occurring in warm clouds, is known to be significantly enhanced by turbulence. Whether particles collide depends on their flow history, in particular on their encounters with highly intermittent small-scale turbulent structures, which despite their rarity can dominate the overall collision rate. Intuitively, strong vortices may act as slings for inertial particles, leading to intersections where several streams of particles collide at large velocities. Here, we develop a quantitative criterion for sling events based on the velocity gradient history along particle paths. We demonstrate by combination of theory and simulations that the problem reduces to a one-dimensional localization problem as encountered in condensed matter physics. The reduction demonstrates that the creation of slings is completely controlled by the smallest negative eigenvalue of the velocity gradient tensor. We use fully resolved turbulence simulations to confirm our predictions and study their Stokes and Reynolds number dependence. We also discuss extrapolations to the parameter range relevant in clouds, showing that sling events at high Reynolds numbers are significantly enhanced for small Stokes numbers.