A Quasi-Liquid Mediated Continuum Model of Faceted Ice Dynamics

We present a quasi-liquid mediated continuum model for ice growth consisting of partial differential equations informed by molecular dynamics simulations. The main insight from molecular dynamics is the appearance of periodic variations in the equilibrium vapor pressure and quasi-liquid thickness of the ice/vapor interface. These variations are incorporated in the continuum model as subgrid scale microsurfaces. We show that persistent faceted ice growth in the presence of inhomogeneities in the ambient vapor field is due to a spontaneous narrowing of terraces at facet corners, which compensates for higher ambient water vapor density via feedback between surface supersaturation and quasi-liquid thickness. We argue that this emergent behavior has the mathematical structure of a stable limit cycle and characterize its robustness in terms of ranges of parameters that support it. Because the model is relevant in the high-surface-coverage regime, it serves as a useful complement to the Burton-Cabrera-Frank framework. Quantitative aspects and limitations of the model are also discussed. © 2016. American Geophysical Union. All Rights Reserved.