Numerical computations of facetted pattern formation in snow crystal growth

TL;DR

This paper introduces a new numerical method to simulate facetted snow crystal growth, capturing diverse natural forms and revealing insights into the effects of supersaturation and surface energy on crystal morphology.

Contribution

The authors develop a novel computational approach enabling detailed 2D and 3D simulations of anisotropic snow crystal growth, including complex morphologies previously difficult to model numerically.

Findings

Tip velocity linearly related to supersaturation

Surface energy effects are more significant than previously thought

First-time numerical simulations of various snow crystal forms

Abstract

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.