Scale-dependent droplet clustering in turbulent clouds

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Abstract
The current understanding of fundamental processes in atmospheric clouds, such as nucleation, droplet growth, and the onset of precipitation (collision–coalescence), is based on the assumption that droplets in undiluted clouds are distributed in space in a perfectly random manner, i.e. droplet positions are independently distributed with uniform probability. We have analysed data from a homogeneous cloud core to test this assumption and gain an understanding of the nature of droplet transport. This is done by examining one-dimensional cuts through clouds, using a theory originally developed for x-ray scattering by liquids, and obtaining statistics of droplet spacing. The data reveal droplet clustering even in cumulus cloud cores free of entrained ambient air. By relating the variance of droplet counts to the integral of the pair correlation function, we detect a systematic, scale-dependent clustering signature. The extracted signal evolves from sub- to super-Poissonian as the length scale increases. The sub-Poisson tail observed below mm-scales is a result of finite droplet size and instrument resolution. Drawing upon an analogy with the hard-sphere potential from the theory of liquids, this sub-Poisson part of the signal can be effectively removed. The remaining part displays unambiguous clustering at mm- and cm-scales. Failure to detect this phenomenon until now is a result of the previously unappreciated cumulative nature, or ‘memory,’ of the common measures of droplet clustering.