Diffusion growth of solid and hollow hexagonal ice columns

Hexagonal ice columns are one of the main ice crystal types in atmospheric clouds and they can be solid or hollow. It has been found that about 90% of ice columns found in cirrus clouds is the hollow type. The diffusion growth rate of hollow ice columns has not been studied rigorously and compared with that of the solid columns. This study examines the diffusion growth of stationary hexagonal ice columns under a specified environmental condition. We use the ice capacitances calculated recently by Chiruta and Wang and consider the effect of both aspect ratio and the degree of hollowness so as to understand their impacts on the growth.

With the assumption that the growth is along c-axis only, the analytical solutions of the linear growth rates for both solid and hollow columns are obtained. The results show that, with the same initial size of 10ƒÝm in diameter and 30 ƒÝm in length, the length of the hollow column grows to 6 times that of the solid one.

We then relax the above assumption by allowing growth along both a- and c-axis and the growth rates are determined by numerical methods. Following a specified power law-type length-diameter relation, comparing 3 cases (solid, half-hollow and total-hollow/sheath) shows the positive feedback of length growth due to the fact that ice capacitance is proportional to length dimension and dimension grows faster in hollow column while the mass growth rates are the same. After 6000 seconds, the sheath gets 1.3 times longer length and 1.7 times larger cross-section-area than solid column, but only 85% equivalent depth (volume/area) of the solid column.

Comparing different aspect ratios for the solid cases, the results show that the larger the aspect ratio (length/diameter), the faster the linear growth rate. After 6000 seconds, a column with aspect ratio 10 grows to 6.4 times longer and 4 times greater cross-sectional area than one with aspect ratio 1.

Implications of the above results on the ice cloud development and their possible climatic impacts will be discussed in the paper.