Modeling snow-crystal growth: A three-dimensional mesoscopic approach

Janko Gravner and David Griffeath
Phys. Rev. E 79, 011601 – Published 6 January 2009

Abstract

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

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  • Received 11 April 2008

DOI:https://doi.org/10.1103/PhysRevE.79.011601

©2009 American Physical Society

Authors & Affiliations

Janko Gravner*

  • Mathematics Department, University of California, Davis, California 95616, USA

David Griffeath

  • Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA

  • *gravner@math.ucdavis.edu
  • griffeat@math.wisc.edu

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Vol. 79, Iss. 1 — January 2009

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