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Collisional growth of droplets, such as occurring in warm clouds, is known tobe significantly enhanced by turbulence. Whether particles collide depends ontheir flow history, in particular on their encounters with highly intermittentsmall-scale turbulent structures, which despite their rarity can dominate theoverall collision rate. Intuitively, strong vortices may act as slings forinertial particles, leading to intersections where several streams of particlescollide at large velocities. Here, we develop a quantitative criterion forsling events based on the velocity gradient history along particle paths. Wedemonstrate by combination of theory and simulations that the problem reducesto a one-dimensional localization problem as encountered in condensed matterphysics. The reduction demonstrates that the creation of slings is completelycontrolled by the smallest negative eigenvalue of the velocity gradient tensor.We use fully resolved turbulence simulations to confirm our predictions andstudy their Stokes and Reynolds number dependence. We also discussextrapolations to the parameter range relevant in clouds, showing that slingevents at high Reynolds numbers are significantly enhanced for small Stokesnumbers.

Quantitative prediction of sling events in turbulence at high Reynolds numbers