| Summary: | Understanding the dynamics of marine ice sheets is integral to studying the evolution of the Antarctic Ice Sheet in both the short and long terms. An important component of the dynamics, grounding line migration, has proved difficult to represent in numerical models, with undesirable behavior such as sensitivity to grid resolution having been observed. Most successful attempts at representing grounding line migration have made use of techniques that are only readily applicable to flowline models, such as Arbitrary Lagrangian-Eulerian schemes. It remains unclear whether a purely Eulerian flowline model can reproduce the actual solution of the governing differential equations, as well as what the theoretical properties of that solution are. In addition, in order to capture the stress transmission involved in another important dynamic component, the buttressing of a marine ice sheet by its ice shelf, the transverse flow direction must also be resolved. Here a numerical model is developed that solves the time-dependent Shelfy-Stream equations [MacAyeal, 1989] and makes use of mesh adaption techniques to overcome the difficulties typically associated with the numerics of grounding line migration. In the special case of a flowline model, it is shown that the Shelfy-Stream equations have a unique solution provided constraints on the initial condition and the forcing are satisfied, and the convergence properties of the model are examined. Model output is also compared with a recent benchmark for flowline models. It is shown that our model yields an accurate solution while using far less resources than would be required without mesh adaption. It is also shown that the mesh adapting techniques extend to two horizontal dimensions. Experiments are carried out to determine how both ice shelf buttressing and ice rises affect the marine instability predicted for an ice sheet on a foredeepened bed. It is found that buttressing is not always sufficient to stabilize such a sheet but collapse of the grounded portion is still greatly delayed. It is also shown that the effect of an ice rise is similar to that of narrowing the ice shelf.
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