Diffusion growth of solid and hollow hexagonal ice columns

The diffusion growth of solid and hollow hexagonal ice columns in clouds is investigated. Two modes are examined: the c-axis only growth and the power law type growth. An analytic expression is obtained for the c-axis only mode and a numerical procedure is developed for the power law type growth. The results show that the hollow columns grow very rapidly compared to the solid ones in the c-axis only growth and length ratio increases quasi-exponentially with time. This rapid growth may be relevant in the initial stage of cirrus development where water vapor is relatively abundant, but other environmental factors will soon set in to limit this mode of growth. The power law type mode results in much slower growth and eventually leads to a quasi-constant ratio growth for hollow versus solid columns. We suggest that the actual growth mode in cirrus may be somewhere between these two limiting cases.