Theories of Competitive Cloud Droplet Growth and Their Application to Cloud Physics Studies

Abstract

In a rising cloud parcel, a small droplet establishes quasi-steady-state fields of vapor density ? and temperature T around it, approximately satisfying the common relationship, ?2?=?2T=0, where ?2 is the Laplacian operator. The fields at this stage merely transfer vapor and heat between the droplet surface and the infinite environment without changing their distributions in space; lowering of ? and T fields is primarily due to cloud parcel lifting and not by the droplet growth. As the growth continues, the fields begin to compete with others of adjacent droplets and limit their expanse within each territory referred to as ?cell.? The supersaturation reaches the maximum shortly thereafter, and the growth mode becomes totally competitive. Under this cell boundary-controlled competitive kinetics, the fields establish a new steady state and transfer properties between the droplet surface and the space inside the cell where ?2? and ?2T take nonzero constant values. Under this condition, the ? and T fields are lowered due to both parcel lifting and droplet growth. To evaluate the difference between the droplet growth of conventional theories and the competitive growth under steady-state conditions, equations describing the latter vapor and temperature fields as well as the mass growth rates are analytically obtained in closed forms under both Maxwellian and diffusion-kinetic conditions. A factor responsible for the competitive kinetics is identified as a function of only the ratio between the droplet radius and the distance between the droplet center and the boundary with the surrounding droplets. Deviation of droplet mass growth rate for the competitive kinetics from that for noncompetitive growth is found to be negligible under the ordinary range of cloud conditions. However, it is pointed out that under unusual situations, laboratory processes in particular, consideration of the deviation may become necessary.