Quantitative prediction of sling events in turbulence at high Reynolds 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.

References in corpus (4)

• Sling effect in collisions of water droplets in turbulent clouds
• An Efficient Particle Tracking Algorithm for Large-Scale Parallel Pseudo-Spectral Simulations of Turbulence
• Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
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Cited by in corpus (4)

• Statistical models for the dynamics of heavy particles in turbulence
• Caustic formation in a non-Gaussian model for turbulent aerosols
• Caustics of finitely dense inertial particles
• Active Caustics