Abstract
Abstract. Warm rain in real clouds is produced by the collision and coalescence of an initial population of small droplets. The production of rain in warm cumulus clouds is still one of the open problems in cloud physics, and although several mechanisms have been proposed in the past, at present there is no complete explanation for the rapid growth of cloud droplets within the size range of diameters from 10 to 50 μm. By using a collection kernel enhanced by turbulence and a fully stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. When the runaway droplet forms, the traditional calculation using the kinetic collection equation is no longer valid, since the assumption of a continuous distribution breaks down. There is in essence a phase transition in the system from a continuous distribution to a continuous distribution plus a runaway droplet. This transition can be associated to gelation (also called sol–gel transition) and is proposed here as a mechanism for the formation of large droplets required to trigger warm rain development in cumulus clouds. The fully stochastic turbulent model reveals gelation and the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol–gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value) reaches its maximum value. Moreover, we show that the non-turbulent case does not exhibit the sol–gel transition that can account for the impossibility of producing raindrop embryos in such a system. In the context of cloud physics theory, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the population and becomes the embryo for runaway raindrops.
Highlights
Whether the formation of large droplets trigger the production of rain in warm cumulus clouds remains one of the open problems in cloud physics
In this study we focus on a model for the growth of cloud droplets by a fully stochastic turbulent collision–coalescence process and we will show that this model reveals a sol– gel transition in the system and the formation of runaway droplets
The total mass in the system (M1) starts to decrease. This is usually interpreted to mean that a macroscopic runaway droplet has formed and the system exhibits a phase sol– gel transition. After this point in time, the average calculated from the stochastic process will differ from the average obtained from the KCE (Eq 1), and there is a transition from a system with a continuous droplet distribution to one with a continuous distribution plus a massive runaway droplet
Summary
Whether the formation of large droplets trigger the production of rain in warm cumulus clouds remains one of the open problems in cloud physics. Many other studies include droplet coalescence as an important factor, mainly through two mechanisms: (i) the collision of large droplets growing on giant and ultra-giant nuclei, and (ii) the self-broadening of the droplet spectra by collisions between cloud droplets. Regarding this second mechanism, it has been emphasized by experimental (Vohl et al, 1999) and theoretical (Pinsky et al, 1999, 2000) studies that there is a significant acceleration of droplet growth rate by collisions in a turbulent flow, with collision efficiencies that may reach values 10 times larger than in the pure gravity case.
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