The Formation of Lake Stars

Abstract

Star patterns, reminiscent of a wide range of diffusively controlled growth forms from snowflakes to Saffman-Taylor fingers, are ubiquitous features of ice covered lakes. Despite the commonality and beauty of these ``lake stars'' the underlying physical processes that produce them have not been explained in a coherent theoretical framework. Here we describe a simple mathematical model that captures the principal features of lake-star formation; radial fingers of (relatively warm) water-rich regions grow from a central source and evolve through a competition between thermal and porous media flow effects in a saturated snow layer covering the lake. The number of star arms emerges from a stability analysis of this competition and the qualitative features of this meter-scale natural phenomena are captured in laboratory experiments.