| Summary: | The polar regions are changing dramatically. The Arctic ocean has seen an increasing fraction of young seasonal sea ice, which contains a relatively high fraction of liquid brine inclusions, and decreasing fraction of older multi-year ice. The binary mixture of solid ice crystals and liquid brine which forms sea ice is both porous and reactive, and can be classified as a mushy layer. Convection within porous sea ice rejects dense brine into the underlying ocean, where it provides an important buoyancy forcing, and circulates nutrients within the ice with consequences for the local biogeochemistry. In this thesis I aim to build understanding of convective processes within sea ice and other mushy layers. I develop a code for direct numerical simulations in two and three dimensions, which uses adaptive mesh refinement to efficiently resolve the key dynamical features across multiple scales by solving mesoscopic conservation equations. This code is then applied to a variety of settings, whilst focussing on the relatively unexplored far-from eutectic limit which is particularly relevant to sea ice. In this far-from eutectic limit the porosity is small except for a narrow porous layer near the mush-liquid boundary. New scaling laws are found for steady-state growth, where the convection is confined to this porous layer whilst the mush-liquid solute flux scales sublinearly with the Rayleigh number - a dimensionless parameter which characterises the ratio of buoyancy to dissipative forces. Simulations of transient growth from a fixed boundary provide new insights into the dynamics and spacing of brine channels, and I find that flow in 3-D is qualitatively similar to 2-D. Meanwhile, I find evidence that convection within warming sea ice may lead to periods of intense salt fluxes into the ocean. These results have important geophysical implications for the dynamics and biogeochemistry of the polar regions.
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