3D Mushy-Layer Convection and Phase Change during the Solidification of Binary Alloys

The solidification of binary alloys is central to a range of geophysical and geological settings, including sea-ice formation by freezing of the polar oceans, solidification in magma chambers and the Earth's inner core, and the evolution of planetary ice shells such as Enceladus. Solidification in these two-component systems often leads to the formation of a mushy layer: a porous mixture of solid crystals and interstitial fluid with varying solute concentration. For example, sea ice is a mushy layer of solid ice crystals and liquid saline brine. The dense brine tends to sink through the ice, driving convection. Downwelling at the edge of convective cells leads to the development of narrow, entirely liquid brine channels. The channels provide an efficient pathway for drainage of the cold, saline brine into the underlying ocean. This brine rejection provides an important buoyancy forcing on the ocean, and causes variation of the internal structure and properties of sea ice on seasonal and shorter timescales. This process is inherently multiscale, with simulations requiring resolution from O(mm) brine-channel scales to O(m) mushy-layer dynamic scales.

We present fully 3-dimensional numerical simulations of mushy layer growth and convective solute fluxes that model flow through a reactive porous solid matrix with evolving porosity. To accurately resolve the wide range of dynamical scales, our simulations exploit Adaptive Mesh Refinement using the Chombo framework. For an application to salt fluxes from sea ice, this allows us to integrate over several months of ice growth, providing insights into mushy-layer dynamics throughout the winter season. During the early stages of ice growth, a dense array of convection cells control flow through the full depth of the ice. The convective desalination of the ice promotes increased internal solidification. As the permeability of the ice decreases, the flow becomes restricted to a narrow porous layer at the ice-ocean interface, with the notable exception of a sparse network of larger brine channels which persist through the full depth of the ice. We investigate the transition between these two regimes and the properties of the larger channels, considering the implications for ice-ocean interactions, sea ice biogeochemistry, and other geophysical mushy layers.