Stability Analysis of Ice Crystal Orientation

Abstract

The stability of ice crystal orientation is studied by modeling the air flow 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 θ e 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.