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

• Flow fields around inclined ice crystals were numerically studied.
• Inclination leads to less spiral rotation of streamlines behind the crystals.
• Inclination enhances vorticity at the upstream and downstream sides.
• We provide parameterization of the hydrodynamic torques acting on the crystals.
• Crystals of millimeter size require 120 kV/m for the electrical alignment to occur.

The flow field and orientation of ice particles are fundamental information to understand cloud microphysical processes, optical phenomena, and electric-field induced orientation and to improve 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 airflow. 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 the one without inclination. For plates, a high-pressure dome on the center of the lower basal face disappears with inclination, possibly leading to an increase of riming there. The torques acting on the crystals have a local maximum over the inclined angle and exhibit almost symmetric around 45° over the range of Reynolds numbers. The torque parameterization was performed under pressures 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 the one for columns. Furthermore, the torque formula was 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 agrees with previous studies.