A Theoretical Determination of the Capture Efficiency of Small Columnar Ice Crystals by Large Cloud Drops

Abstract

A theoretical model has been formulated to study by numerical techniques the efficiency E with which columnar ice crystals grown at temperatures between ?3 and ?8°C are captured in a cloud by relatively large, supercooled cloud drops. The ice crystals studied had lengths L of 15 ≤ L ≤ 240 ?m and diameters D of 1.5 ≤ D 240 ?m. and L/D values of 1.0, 3.0 and 10.0. The specific gravity of the ice crystals was assumed to be 0.92 and 0.5 g cm?3. The cloud drops had Reynolds numbers of 10, 30, 100, ?200, 300 and 400, corresponding to the drop radii rd of 100, 165, 300, 416, 510 and 591 ?m in air at. 900 mb and ?6°C. A few computations were made for 500 mb and ?10°C. The ice crystals were assumed to have three typical, yet fixed, orientations with respect to the drop, in an attempt to take into account, in an idealized manner, the different orientations a columnar ice crystal assumes as it moves around a failing drop. It is found that a water drop of given size collects columnar ice crystals with an efficiency which decreases with decreasing length L of the crystal, with increasing length-to-diameter ratio L/D, and with decreasing bulk density ?c of the crystal. Increasing height in the atmosphere (coupled to decreasing pressure and corresponding decreasing temperature) increases the collision efficiency. Considering the fact that columnar ice crystals in atmospheric clouds exhibit length-to-width ratios L/D which approach unity as L becomes smaller, our results show that for drops of 100 ≤ rd ≤ 600 ?m, 0.9 ≤ E ≤ 1.0 for all ?warm region? (?3 to ?8°C) columnar atmospheric ice crystals grown at relatively low supersaturations. For needle crystals, which may grow in the same temperature range but at high supersaturations, E may assume values which are considerably below 1.0. For a drop of a given size, colliding with an ice crystal of a given mass, E was found to be generally higher if the drop collided with a spherical ice crystal than if it collided with a columnar crystal. The orientation of the columnar crystal with respect to the collector drop was found to have only a small effect on E.