Evaluating Droplet Size Distribution Evolution with Different Hydrodynamic Collision Kernels in Turbulent Clouds.

The evolution of cloud droplet size distributions (DSDs) through collision–coalescence is governed by the Smoluchowski coagulation equation (SCE), which becomes analytically intractable when realistic kernels incorporating turbulence and hydrodynamic interactions are used. In this study, we examine DSD evolution using physically motivated kernels that account for bidisperse droplet interactions influenced by gravitational settling and turbulence-induced relative motion. A high-order, mass-conserving Bott-type flux scheme is implemented to numerically solve the SCE and evaluate scale-dependent behaviours such as mass flux and convergence across droplet sizes. Special emphasis is placed on hydrodynamic kernels derived from first principles, incorporating accurate lubrication physics and van der Waals forces relevant for droplets undergoing differential sedimentation in a turbulent background. The resulting DSDs are analysed to identify possible steady-state or self-similar solutions, yielding a detailed characterisation of droplet growth dynamics in turbulent cloud environments.