Drop Inertia and Its Contribution to Turbulent Coalescence in Convective Clouds. Part I: Drop Fall in the Flow with Random Horizontal Velocity

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Abstract
The results of simulated drop fall in horizontal flows with the vertical shear of different kinds (constant linear, periodic, and with random velocity distribution) are presented. It is shown that the inertia of drops is significant enough to lead to substantial drop velocity deviations from the velocity of the flow and to the generation of relative velocity between drops of different sizes. For small droplet the velocity difference caused by turbulence is of the same order as the difference in terminal fall velocities. The results of calculations of drop fall through the horizontal flow with the random Kolmogorov spectrum distribution of velocity indicate that a comparable impact of turbulence in this flow is significant for the whole spectrum of drop sizes and that it even increases for small droplets. The increase of the relative velocity between interacting drops is interpreted as an increase in the swept volume and an increase of a number of drop collisions per unit of times. Thus, in the commonly used expression for the collision kernel, the difference between terminal velocities was replaced by the mean square root relative velocity difference. Simulation of drop spectrum evolution using the stochastic coalescence equation indicates that cloud turbulence significantly influences warm rain initiation and development even when the collision efficiencies obtained in still air are used. The results also show that the difference in the horizontal components of drop velocities in a turbulent cloud can contribute significantly to the rain formation process. Hence, we have to keep in mind the “horizontal” coalescence in convective clouds along with the commonly considered “vertical” coalescence.

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