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Numerical Study of Motion and Stability of Falling Columnar Crystals

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  • 1 Research Center for Environmental Changes, Academia Sinica, Nankang, Taipei, Taiwan
  • 2 Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin
  • 3 Research Center for Environmental Changes, Academia Sinica, Nankang, Taipei, Taiwan
  • 4 Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin, and Research Center for Environmental Changes, Academia Sinica, Nankang, Taipei, Taiwan
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Abstract

Understanding of the flow field and falling patterns of ice crystals is fundamental to cloud physics and radiative transfer, and yet the complex shape hampers a comprehensive understanding. In order to create better understanding of falling patterns of columnar crystals, this study utilizes a computational fluid dynamics package and explicitly simulates the motion as well as the flow fields. Three modes of patterns (i.e., strong damping, fluttering, and unstable modes) were identified in the space of inverse aspect ratio (q) and Reynolds number (Re). The boundary of stability depicts the “L” shape as found in a previous experimental study. This study newly found that the range of Re for stable motion increases with a decrease in q. Decomposition of hydrodynamic torques indicates that, for stable mode, the pressure and viscous torques acting on the lower prism faces counteract the rotation when the inclination angle becomes 0°. The unstable motion was attributed to the pressure torque acting on the upper prism faces, which is associated with eddies that lag behind the oscillating boundary. Observed Re–q relationships of columns suggest that the strong damping mode is most likely to occur in the atmosphere, but the fluttering mode is also possible. Furthermore, the time scales of oscillation and damping were parameterized as a function of q and Re. The impact of the fluttering on the riming process is limited at the beginning, which supports the current formulation in numerical weather and climate models.

Current affiliation: Research Institute for Applied Mechanics, Kyushu University, Kasuga, Japan.

Corresponding author address: Dr. Pao K. Wang, Dept. of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: pwang1@wisc.edu

Abstract

Understanding of the flow field and falling patterns of ice crystals is fundamental to cloud physics and radiative transfer, and yet the complex shape hampers a comprehensive understanding. In order to create better understanding of falling patterns of columnar crystals, this study utilizes a computational fluid dynamics package and explicitly simulates the motion as well as the flow fields. Three modes of patterns (i.e., strong damping, fluttering, and unstable modes) were identified in the space of inverse aspect ratio (q) and Reynolds number (Re). The boundary of stability depicts the “L” shape as found in a previous experimental study. This study newly found that the range of Re for stable motion increases with a decrease in q. Decomposition of hydrodynamic torques indicates that, for stable mode, the pressure and viscous torques acting on the lower prism faces counteract the rotation when the inclination angle becomes 0°. The unstable motion was attributed to the pressure torque acting on the upper prism faces, which is associated with eddies that lag behind the oscillating boundary. Observed Re–q relationships of columns suggest that the strong damping mode is most likely to occur in the atmosphere, but the fluttering mode is also possible. Furthermore, the time scales of oscillation and damping were parameterized as a function of q and Re. The impact of the fluttering on the riming process is limited at the beginning, which supports the current formulation in numerical weather and climate models.

Current affiliation: Research Institute for Applied Mechanics, Kyushu University, Kasuga, Japan.

Corresponding author address: Dr. Pao K. Wang, Dept. of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: pwang1@wisc.edu
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