Glacier and ice sheet dynamics

Glaciers and ice sheets are thin viscous gravity currents subject to mass sources and sinks due to surface snow accumulation and melting. Mathematically, the evolution of glacier geometry poses interesting free boundary problems. Land-based glaciers and ice sheets can be described by a parabolic obstacle problem which aids the development of numerical methods for tracking the free boundary. I will discuss one simple algorithm for computing the evolving shape of a land-based glacier, and compare results with known analytical solutions. Marine ice sheets (Antarctica being an example) stand apart fromt their land-based counterparts because their edge is located not where ice thickness goes to zero, but where it attains a locally defined critical thickness. I will discuss how the migration of the ice sheet edge in that case is controlled by a stress boundary layer, and compare numerical results that resolve the boundary layer with analytical ones that arise from applying perturbation methods. Finding good agreement, I will also discuss the large-scale behaviour of marine ice sheets as thin-film flows with free boundaries, focusing on the effect of forcing parameters on their steady-state configurations.