Search

Pound for pound, sea ice is the most important component of Earth's climate system. The changing conditions in which sea ice forms and exists are likely to affect the properties of sea ice itself, and potential climate feedbacks need to be identified and understood to improve future projections. Here we perform a set of idealised experiments which model sea ice growth under a range of ambient salinities, freezing temperatures, and freezing orientations. The results confirm existing theories; sea ice growth rate is largest for cooler freezing temperatures, fresher ambient salinities, and bottom oriented freezing configuration. Our primary metric of interest is the brine mass fraction (the mass ratio of brine inclusions to the total sea ice), which we quantify and determine the sensitivity of with respect to changes in freezing conditions. We find that the brine mass fraction of our model sea ice is most sensitive to freezing temperature, and increases 2.5% per 1oC increase of freezing temperature. This finding suggests that future sea ice in warmer climate states will retain more brine, with subsequent flow on effects for circulations driven by brine rejection in the high-latitude oceans.

We derive a thermodynamically consistent model for phase change in sea ice by adding salt to the framework introduced by Penrose and Fife. Taking the salt entropy relative to the liquid water molar fraction provides a transparent mechanism for salt rejection under ice formation. We identify slow varying coordinates, including salt density relative to liquid water molarity weighted by latent heat, and use multiscale analysis to derive a quasi-equilibrium Stefan-type problem via a sharp interface scaling. The singular limit is under-determined and the leading order system is closed by imposing local conservation of salt under interface perturbation. The quasi-steady system determines interface motion as balance of curvature, temperature gradient, and salt density. We resolve this numerically for axisymmetric surfaces and show that the thermal gradients typical of arctic sea ice can have a decisive impact on the mode of pinch-off of cylindrical brine inclusions and on the size distribution of the resultant spherical shapes. The density and distribution of inclusion sizes is a key component of sea ice albedo which factors into global climate models.

We analyze the competitive evolution of codimension one and two morphologies within the $H^{-1}$ gradient flow of the strong Functionalized Cahn-Hilliard equation. On a slow time scale a sharp hypersurface reduction yields a degenerate Mullins-Sekerka evolution for both codimension one and two hypersurfaces, leading to a geometric flow that depends locally on curvatures couples to the dynamic value of the spatially constant far-field chemical potential. Both codimension one and two morphologies admit two classes of bifurcations, one leads to pearling, a short-wavelength in-plane modulation of interfacial width, the other flips motion by curvature to the locally-ill posed motion against curvature, which leads to fingering instabilities. We present a bifurcation diagram for the morphological competition, and compare our results quantitatively to simulations of the full system and qualitatively to simulations of self-consistent mean field models and laboratory experiments; illuminating the role of the pearling bifurcation in the development of complex network morphologies.

The Functionalized Cahn-Hilliard free energy supports phase separated morphologies of distinct codimension, including codimension-one bilayer and codimension-two filament morphologies. We characterize the linear stability of bilayer and filament morphologies associated to hypersurfaces within the strong functionalization scaling. In particular we show that the onset of the pearling instability, which triggers fast in-plane oscillations associated to bifurcation to higher codimensional morphology, is controlled by the functionalization parameters and the spatially constant value of the far-field chemical potential. Crucially, we show that onset of pearling is independent of the shape of the defining hypersurface.