Turbulent Collision-Coalescence of Cloud Droplets and its Impact on Warm Rain Formation

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The PIs are seeking to quantify the effects of turbulence on the collection kernel of cloud droplets and how this impacts the warm rain precipitation process. Air turbulence could affect the collection kernel through (1) enhanced relative motion due to differential acceleration and shear effects, (2) enhanced average pair density due to local clustering of droplets, and (3) enhanced collision efficiency due to turbulent fluctuations. The levels of enhancements depend, in a complex manner, on the size of droplets (which in turn determines the response time and settling velocity) and the strength of air turbulence as measured by the flow dissipation rate and Reynolds number.The first objective of this research is to parameterize the above effects of turbulence by combining a Hybrid Direct Numerical Simulation (HDNS) approach and a theoretical approach. The HDNS approach integrates an improved superposition method for the disturbance flows due to droplets into a pseudo-spectral simulation of undisturbed air turbulence. This allows for the direct incorporation of hydrodynamic interactions within DNS and computations from first principles of all statistical information related to collision-coalescence. The theoretical approach is based on a successive pair-trajectory approximation and probability distribution function modeling of pair statistics, and will be used to model Reynolds-number effects. The deliverable will be a parameterized collection kernel for different droplet-pair size combinations, flow dissipation rates, and Reynolds numbers. Realistic flow conditions from cumulus cloud observations, e.g., the Small Cumulus Microphysics Study (SCMS) and the Rain In Cumulus over the Ocean (RICO) experiment, will be used in this investigation.The second objective is to study the effects of turbulence on the broadening rate of droplet size spectrum by numerically integrating the kinetic collection equation (KCE) within cloud models, using the enhanced collection kernel developed above. In particular, we will study the time scale during which drizzle drops can be generated from initially narrow size distribution. Our approach is to combine our recently developed numerical method (Linear integral method with Gauss quadrature) for treating KCE with a warm precipitating cloud model (a rising parcel). The goal is to understand and quantify the connection between the above effects of turbulence with observations in warm precipitating clouds.Broader impacts of the research: The research intends to resolve the outstanding question of whether the air turbulence can reconcile the discrepancy between the existing model predictions and observations in cumulus clouds (the size-gap problem). Critical weather phenomena such as aircraft icing and freezing precipitation resulting from warm rain processes are known to have a significant economical impact. The research will also impact other areas of atmospheric science and engineering: such as indirect aerosol effects on weather and climate, spray combustion, powder production, and industrial emissions. The interdisciplinary team from the University of Delaware and the National Center for Atmospheric research allows new theoretical developments and advanced engineering research tools to be efficiently applied to atmospheric processes. The research offers two graduate students and one undergraduate minority student a unique educational experience as they take advantage of the resources at both institutions.