Numerical approaches to droplet growth in atmospheric turbulence

• Main Author: Li, Xiang-Yu
• Format: Others
• Language: English
• Published: Stockholms universitet, Meteorologiska institutionen (MISU) 2016
• Subjects: turbulence; coagulation; condensation; rain formation; Earth and Related Environmental Sciences; Geovetenskap och miljövetenskap
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-129868; http://nbn-resolving.de/urn:isbn:978-91-7649-440-0

The bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by con-densation nor gravitational collision in the size range of 15–40 μm in radius. Turbulence-generated collision has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study develops the numerical approaches to study droplet growth in atmospheric turbulence and investigates the turbulence effect on cloud droplet growth. The collision process of in-ertial particles in turbulence is strongly nonlinear, which motivates the study of two distinct numerical schemes. An Eulerian-based numerical formulation for the Smoluchowski equation in multi-dimensions and a Monte Carlo-type Lagrangian scheme have been developed to study the combined collision and condensation processes. We first investigate the accuracy and reliability of the two schemes in a purely gravitational field and then in a straining flow. Discrepancies between different schemes are most strongly exposed when con-densation and coagulation are studied separately, while their combined effects tend to result in smaller discrepancies. We find that for pure collision simulated by the Eulerian scheme, the mean particle radius slows down using finer massbins, especially for collisions caused by different terminal velocities. For the case of Lagrangian scheme, it is independent of grid resolution at early times and weakly dependent at later times. Comparing the size spectra simulated by the two schemes, we find that the agreement is excellent at early times. For pure condensation, we find that the numerical solution of condensation by the Lagrangian model is consistent with the analytical solution in early times. The Lagrangian schemes are generally found to be superior over the Eulerian one interms of computational performance. Moreover, the growth of cloud droplets in a turbulent environment is investigated as well. The agreement between the two schemes is excellent for both mean radius and size spectra, which gives us further insights into the accuracy of solving this strongly coupled nonlinear system. Turbulence broadens the size spectra of cloud droplets with increasing Reynolds number.