Quantitative Prediction of Sling Events in Turbulence at High Reynolds Numbers

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. Here, we develop a quantitative criterion for sling events based on the velocity gradient history along particle paths. We show by a 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 controlled by the minimal real 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 for typical cloud droplets, showing that sling events at high Reynolds numbers are enhanced by an order of magnitude for small Stokes numbers. Thus, intermittency could be a significant ingredient in the collisional growth of rain droplets.