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

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.