The convective desalination of sea ice

This thesis aims to improve our understanding of the fundamental processes affecting the growth of sea ice in the polar oceans in order to improve climate models. Newly formed sea ice contains a significant amount of salt as liquid brine in the interstices of an ice matrix. My focus is on one of the processes by which the salt content of sea ice decreases, namely convective desalination, which is also often called gravity drainage by geophysicists. Modelling convective desalination requires an understanding not only of the thermo-dynamics of sea-ice growth but also of its internal fluid dynamics. This thesis considers a class of physical systems called mushy layers, of which sea ice is an example. Mushy layers are multi-component systems consisting of a porous matrix of solid phase whose interstices contain the same substance in the liquid phase. I develop a mathematical description of these systems in terms the of mushy-layer equations and explore the appropriate boundary conditions at a mush-liquid interface. I develop a simple Chimney-Active-Passive (CAP) model of convection in mushy layers for arrays of liquid chimneys in two and three dimensions. This allows the interstitial fluid flow and salt flux from the mushy layer to be determined in terms of the dimensionless parameters of the system. I discuss important mathematical and physical aspects of the CAP model. I then explain the physics of gravity drainage from sea ice, elucidating the connection between downward flow through liquid brine channels (chimneys) and a convective upwelling in the rest of the ice that is sustained by horizontal density differences and provides the fluid to replace that which drains from the ice. I use the CAP model to determine the convective upwelling velocity mathematically, deriving a new, physical parameterization of gravity drainage. I test my predictions by investigating previous laboratory observations of the propagation of dye fronts. Finally, I take a one-dimensional, thermodynamic sea-ice model of the kind currently used in coupled climate models and parameterize convective desalination using the CAP model. The parameterization allows determination of physical properties and salt fluxes from sea ice dynamically, corresponding to the calculated, evolving salinity of the sea ice, in contrast to older, established models that prescribe a fixed salinity. I find substantial differences compared to previous models, particularly in terms of predicted salt fluxes from sea ice. I explain the likely implications and potential advantages of my parameterization for climate models