Vapour condensation in cloud cores produces small droplets that are close to one another in size. Droplets are believed to grow to raindrop size by coalescence due to collision1,2. Air turbulence is thought to be the main cause for collisions of similar-sized droplets exceeding radii of a few micrometres, and therefore rain prediction requires a quantitative description of droplet collision in turbulence1-5. Turbulent vortices act as small centrifuges that spin heavy droplets out, creating concentration inhomogeneities6-14 and jets of droplets, both of which increase the mean collision rate. Here we derive a formula for the collision rate of small heavy particles in a turbulent flow, using a recently developed formalism for tracing random trajectories15,16. We describe an enhancement of inertial effects by turbulence intermittency and an interplay between turbulence and gravity that determines the collision rate. We present a new mechanism, the 'sling effect', for collisions due to jets of droplets that become detached from the air flow. We conclude that air turbulence can substantially accelerate the appearance of large droplets that trigger rain.
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