John W. Barrett, Harald Garcke, Robert Nürnberg
Facetted growth of snow crystals leads to a rich diversity of forms, and
exhibits a remarkable sixfold symmetry. Snow crystal structures result from
diffusion limited crystal growth in the presence of anisotropic surface energy
and anisotropic attachment kinetics. It is by now well understood that the
morphological stability of ice crystals strongly depends on supersaturation,
crystal size and temperature. Until very recently it was very difficult to
perform numerical simulations of this highly anisotropic crystal growth. In
particular, obtaining facet growth in combination with dendritic branching is a
challenging task. We present numerical simulations of snow crystal growth in
two and three space dimensions using a new computational method recently
introduced by the authors. We present both qualitative and quantitative
computations. In particular, a linear relationship between tip velocity and
supersaturation is observed. The computations also suggest that surface energy
effects, although small, have a larger effect on crystal growth than previously
expected. We compute solid plates, solid prisms, hollow columns, needles,
dendrites, capped columns and scrolls on plates. Although all these forms
appear in nature, most of these forms are computed here for the first time in
numerical simulations for a continuum model.
View original:
http://arxiv.org/abs/1202.1272
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