Turbulent collision statistics of cloud droplets at low dissipation rates
Date
2016
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Publisher
University of Delaware
Abstract
Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. In this thesis we present direct numerical simulation (DNS) results for collision statistics of droplets in turbulent flows of low dissipation rates (in the range of 3 cm2/s3–100 cm2/s3) relevant to strato-cumulus clouds.
First, we revisit the case of gravitational collision in still fluid to validate the details of the collision detection algorithm used in our code. We compare the collision statistics with either new analytical predictions regarding the percentages of different collision types, or results from published papers. The effect of initial conditions on the collision statistics and statistical uncertainties are analyzed both analytically and through the simulation data.
Second, we consider the case of weak turbulence (as in strato-cumulus clouds). In this case the particle motion is mainly driven by gravity. The standard deviation (or the uncertainty) of the average collision statistics is examined analytically in terms of time correlation function of the data. We then report new DNS results of collision statistics in a turbulent flow, showing how air turbulence increases the geometric colli- sion statistics and the collision efficiency. We find that the collision-rate enhancement due to turbulence depends nonlinearly on the flow dissipation rate. This result calls for a more careful parameterization of the collision statistics in strato-cumulus clouds.
Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet inertial response time, rather than the time step necessary for the flow simulation. This situation makes the simulations very expensive to perform. With the motivation to speed up the simulations, we implement the asymptotic expansion approach (as in Maxey, 1987) for particle tracking as this method is suitable for low particle Stokes number and avoids the numerical integration of the stiff equation of motion of droplets. We first validate our implementation using the simpler 2-D cellular flow. Next, we compare the collision statistics of the newly implemented asymptotic approach with our existing approach of particle tracking as well as with published results from journal papers. Finally, we provide the run time comparison for both methods.