Pattern Formation in Growth of Snow Crystals: Hexagonal and Dendritic Patterns

Abstract

We simulate the pattern formation in growth of snow crystals, i.e. ice crystals growing from the vapor, by taking into account (1) the surface kinetic process and (2) diffusion process under various growth conditions. Hexagonal patterns are obtained starting from a circular crystal for small supersaturation. On the other hand, dendritic patterns are obtained for large supersaturation. The conditions for the transition from hexagonal to dendritic patterns are given by the supersaturation and the dimensionless crystal size with reference to the mean free path of a water molecule in the vapor.