Effects of correlated collisions and intermittency on the growth of lucky droplets

Titelangaben

Bätge, Tobias ; Zierenberg, Johannes ; Wilczek, Michael:
Effects of correlated collisions and intermittency on the growth of lucky droplets.
In: Proceedings of the National Academy of Sciences of the United States of America. Bd. 123 (2026) Heft 9 . - e2502553123.
ISSN 1091-6490
DOI: https://doi.org/10.1073/pnas.2502553123

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Abstract

Given the complexity of precipitation in warm clouds, simple conceptual models are crucial for identifying key aspects of accelerated droplet growth. Statistical outliers with anomalously frequent collisions, so-called lucky droplets, are commonly assumed to play a central role in explaining the timescales of the onset of precipitation. Here, we investigate how the formation of lucky droplets is accelerated by correlated collisions and turbulence intermittency. Using a non-Markovian stochastic framework, we show that while short-term correlations enhance early growth, dissipation fluctuations dominate the process. Our approach, which models a statistical ensemble of cloud parcels based on turbulent dissipation rates, provides a systematic path for bridging scales between simulations or laboratory studies and atmospheric clouds. To trigger precipitation, water droplets in warm clouds need to attain a sufficient size. Theoretical estimates based on condensation and gravitational collisions alone fail to explain the observed timescales for the onset of precipitation for a range of droplet sizes. This suggests the involvement of collisional growth mediated by turbulence to resolve the so-called “size-gap problem.” For the onset of rain, it is sufficient that statistical outliers, coined “lucky droplets,” cross the size gap. In this study, we explore the influence of turbulence on droplet growth, focusing on correlated collisions and intermittency. Using direct numerical simulations of droplets in turbulent flow, we constrain a non-Markovian stochastic framework that allows us to assess memory effects on the droplet-size distribution arising from correlations between consecutive collisions. Using our framework, we find that correlated collisions accelerate the initial growth of lucky droplets but have subleading effect at later stages. Consequently, we neglect correlations from collisions and model an ensemble of cloud parcels representing fluctuations in the volume-averaged dissipation rate. Here, the distribution of droplet sizes in each parcel is described by a linear master equation with a time-dependent collision rate according to the volume-averaged dissipation rate. Our analyses of this toy model show that intermittency can significantly reduce the time required by lucky droplets to cross the size gap.