Numerical approaches to droplet growth in atmospheric turbulence
Abstract: The bottleneck problem of cloud droplet growth is one of the most challengingproblems 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 bridgethe size gap, i.e., the bottleneck problem. This study develops the numericalapproaches to study droplet growth in atmospheric turbulence and investigatesthe turbulence effect on cloud droplet growth. The collision process of in-ertial particles in turbulence is strongly nonlinear, which motivates the studyof two distinct numerical schemes. An Eulerian-based numerical formulationfor the Smoluchowski equation in multi-dimensions and a Monte Carlo-typeLagrangian scheme have been developed to study the combined collision andcondensation processes. We first investigate the accuracy and reliability of thetwo schemes in a purely gravitational field and then in a straining flow. Dis-crepancies between different schemes are most strongly exposed when con-densation and coagulation are studied separately, while their combined effectstend to result in smaller discrepancies. We find that for pure collision simulatedby the Eulerian scheme, the mean particle radius slows down using finer massbins, especially for collisions caused by different terminal velocities. For thecase of Lagrangian scheme, it is independent of grid resolution at early timesand weakly dependent at later times. Comparing the size spectra simulated bythe two schemes, we find that the agreement is excellent at early times. Forpure condensation, we find that the numerical solution of condensation by theLagrangian model is consistent with the analytical solution in early times. TheLagrangian schemes are generally found to be superior over the Eulerian one interms of computational performance. Moreover, the growth of cloud dropletsin a turbulent environment is investigated as well. The agreement between thetwo schemes is excellent for both mean radius and size spectra, which givesus further insights into the accuracy of solving this strongly coupled nonlinearsystem. Turbulence broadens the size spectra of cloud droplets with increasingReynolds number.
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