Caustic activation of rain showers

TL;DR

This paper demonstrates that turbulence-induced caustics significantly increase droplet collision rates in clouds, providing a quantitative explanation for rapid rainfall onset without relying on particle clustering.

Contribution

It introduces a theory linking turbulence intensity to droplet collision rates via caustic formation, a novel activated process analogy.

Findings

Collision rate increases abruptly at turbulence threshold

Caustic formation rate follows an exponential dependence on Stokes number

Theory explains rapid rainfall onset in convective clouds

Abstract

We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The formation of caustics is an activated process, in which a measure of the intensity of the turbulence, termed the Stokes number St, is analogous to temperature in a chemical reaction: the rate of collision contains a factor exp(-C/St). Our results are relevant to the long-standing problem of explaining the rapid onset of rainfall from convecting clouds. Our theory does not involve spatial clustering of particles.