| Summary: | Sea ice is salt-water ice which forms at the poles when the oceans solidify, and it plays a vital role in polar climate and ecosystems. In particular, the salt fluxes from growing sea ice are a major contributor to the cold halocline in the Arctic, and to the Arctic and Southern Ocean circulations more generally. Sea ice is not a pure solid - it has a microstructure of solid ice crystals and concentrated brine, known as a mushy layer. Segregation occurring during solidification means that the colder interstitial fluid closer to the ice surface also has a larger salinity than the warmer, fresher, underlying ocean. This creates a tendency for convection which drives the observed salt fluxes from growing ice, and provides nutrients fluxes for algae within the sea ice. This thesis aims to characterise the early growth and convective onset in sea ice through a broad investigation of the relevant parameters. The study makes use of the mushy layer equations which describe the transport of mass, energy, salinity, and momentum through a reactive, porous medium. Whilst motivated by sea ice, the results are presented generally, and may have implications for convection problems in Earth sciences and engineering. I investigate the dependence on the dimensionless parameters that characterise the system; with particular focus on the (dimensionless) liquidus gradient and the Biot number. The liquidus gradient describes the ratio of salinity to thermal scales, while the Biot number measures the rate of effective thermal conduction by the surface boundary. This is an aspect which has not previously been considered in growing mushy layers. I identify two clear limiting regimes for growth. When salinity variations are relatively large compared to thermal variations the mushy layer has a high porosity. A second regime, referred to as the Stefan regime, features comparatively smaller salinity variation and substantial internal solidification, with high porosity confined to a narrow region at the mush base. Most sea ice systems ...
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