Numerical simulation of the flow fields around falling ice crystals with inclined orientation and the hydrodynamic torque

Understanding the flow fields and orientation of ice particles are fundamental for understanding cloud microphysical processes and optical phenomena and improving remote sensing of ice clouds. The purpose of this study is to investigate the flow fields and hydrodynamic torques of falling ice columns and hexagonal plates with their largest dimension inclined with respect to the horizontal direction. The Reynolds numbers range from 2 to 70 for columns and 2 to 120 for plates. The flow fields are obtained by numerically solving the relevant Navier-Stokes equations under the assumption of air incompressibility. It was found that for the intermediate Reynolds number the streamlines around the inclined crystals exhibit less spiral rotation behind them than those around the stable posture. The vorticity magnitude was larger in the upstream side and broader in the downstream than one without inclination. For plates, a high-pressure dome on the center of lower basal face disappears with inclination, possibly leading to increase of riming there. The torques acting on the crystals were found to be convex over inclined angles and almost symmetric around 45° over the Reynolds number considered here. The torque parameterization was performed under pressure of 300, 500, and 800 hPa as a function of Reynolds number and aspect ratio. It was found that the time scale of rotation for plates is smaller than one for columns. Furthermore, the torque formula were applied to assess alignment of crystals along electric fields. It was found that these crystals of millimeter size require 120 kV/m for the electrical alignment, which agree with previous studies.