Stability Analysis of Ice Crystal Orientation

Abstract

Abstract The stability of ice crystal orientation is studied by modeling the airflow around ice crystals at moderate Reynolds number, where an ice crystal is approximated by a cylinder with three parameters: diameter D, length L, and zenith angle of the axis θ. In this paper, the torque acting on ice crystals is simulated at different θ first, and then a special θ with zero horizontal torque, denoted as θe, is sought as an equilibrium of ice crystal orientation. The equilibrium is classified into two kinds: stable and unstable. Ice crystals rotate to θe of stable equilibriums while deviating from θe of unstable ones once they are released into quiet air. Multiple equilibriums of ice crystal orientation are found via numerical simulations. A cylinder with D/L close to one has three equilibriums, two of which are stable (i.e., θe = 0° and 90°). A cylinder with D/L away from one has only two equilibriums, one of which is stable (i.e., either θe = 0° or 90°). In addition, an asymmetric cylinder has two, three, or five equilibriums, and their θe is sensitive to the distance between its geometrical center and its center of gravity. The sensitivity of θe to crystal asymmetry suggests large symmetric ice crystals tend to become asymmetric (or irregular) and subsequently oriented randomly. Significance Statement Ice crystal orientation impacts high-cloud reflectance and satellite-based observations of high clouds significantly. However, its laboratory and field observations look dissimilar: the percentage of horizontally oriented ice crystals (HOICs) observed in the laboratory is quite high, while in the field it is often low and varies greatly in space and time. The motivation for this study is to elucidate what causes the difference between the laboratory and field observations. The torque acting on ice crystals are computed by modeling the airflow around ice crystals, revealing the conditions for nonhorizontal orientations of ice crystals. In quiet air, an ice crystal is oriented either horizontally or vertically when its shape is close to sphere. When its shape is elongated in one direction, its orientation depends on its asymmetry in density and shape. The sensitivity of ice crystal orientation to ice crystal asymmetry explains the low percentage of HOICs in the field, because asymmetric ice crystals are common in clouds. As an application, this sensitivity together with the observed percentage of HOICs can be used to infer the processes of ice crystal growth in clouds, providing clues to better representation of ice crystals in weather and climate models.