Abstract
Two models for raindrop growth in clouds are developed and compared. A continuous accretion model is solved numerically for drop growth from 20-50 microns, using a polynomial approximation to the collection kernel, and is shown to underestimate growth rates. A Monte Carlo simulation for stochastic growth is also implemented to demonstrate discrete drop growth. The approach models the effect of decreased average time between captures as the drop size increases. It is found that the stochastic model yields a more realistic growth rate, especially for larger drop sizes. It is concluded that the stochastic model showed faster droplet accumulation and hence shorter times for drop growth.
Highlights
In clouds, the development of a size distribution of rain drops with radius R, as they collect droplets of radius r, is described by a nonlinear differential equation relating the mean number concentration of droplets N(r) to the rate at which drops and droplets collide and coalesce
In this work we developed and compared two models for raindrop growth in clouds based on continuous accretion and stochastic technique by using numerical solution and Monte Carlo simulation
Drop growth have been computed for an initial collector drop radius of Ri = 20 μm and continued until the drop reached a final radius Rf = 50 μm
Summary
The development of a size distribution of rain drops with radius R, as they collect droplets of radius r, is described by a nonlinear differential equation relating the mean number concentration of droplets N(r) to the rate at which drops and droplets collide and coalesce. The super supersaturated created in the updraft is distributed over fewer drops, permitting them to grow to larger sizes. The saturated cannot persist and much less grow unless the environment is supersaturated (H >100%) by the amount equal to the vapor pressure of the droplet by according to Richard et al. When a pair of drops collides they may subsequently: (i) bounce apart, (ii) coalesce and remain so, (iii) coalesce temporarily but break apart, retaining their initial identities, (iv) coalescence temporarily but break apart to a number of smaller drops. For sizes smaller than 100 microns in radius, the important interactions are (i) and (ii), described by Barnet (2011) and Rogers and Yau (1989)
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