Evaluating Droplet Size Distribution Evolution with Physically Based Collision Kernels in Warm Cumulus Clouds

Understanding how cloud droplets transition across the “size gap” between condensational growth and efficient gravitational collection remains central to predicting warm-rain formation in turbulent clouds. We examine this transition by solving the Smoluchowski Coagulation Equation with a high-order, mass-conserving flux scheme and by comparing a suite of physically grounded hydrodynamic collision kernels. These kernels combine differential settling with turbulence-driven relative motion and explicitly account for near-field interactions—non-continuum lubrication forces and van der Waals attraction—that strongly influence coalescence at small separations. By diagnosing the evolution and convergence of mass flux across droplet sizes, we assess how different kernel formulations accelerate or delay growth through the bottleneck regime and whether the resulting distributions exhibit quasi-steady or self-similar structure. The study provides quantitative insight into how turbulence-modified microphysical interactions shape droplet size distributions and ultimately regulate warm-rain initiation in atmospheric clouds.