In this thesis, I explore the flow dynamics associated with ice shelves confined within channels and the buttressing they provide to grounded ice. Ice shelves are the floating extensions of ice sheets and act as the interface between the ice sheet and the ocean. They form when ice flows out from the interior of the ice sheet towards the coast and begins to float as the ice thins. Ice shelves are often found within a channel or pinned in place by stationary bedrock outcrops. The interest in their dynamics is motivated by the buttressing effect they provide to the grounded ice, which strongly controls the rate of ice discharge and thereby the contribution to sea-level rise. I use a combination of mathematical modeling, fluid-mechanical laboratory experiments and geophysical data analysis to develop an improved understanding of ice-shelf flow dynamics.

Initially, geophysical data in the form of Antarctic ice-surface velocity data is analysed, producing maps of strain rate, shear rate and strain orientation for Antarctic ice shelves. This allows the geophysical setting and flow processes to be explored, particularly by identifying areas where resistance to ice flow is generated and regions of the shelf that make no contribution to buttressing. Using the geophysical data, I find good agreement between a theoretical scaling relationship for ice flow at the ice-shelf calving front and data from Antarctic ice shelves.

I proceed to develop an idealized mathematical model of an ice shelf confined to flow in a channel. By assuming shear-dominated dynamics within the shelf, analytical solutions are obtained for steady-state ice-shelf thickness profiles in parallel and diverging channels. This model is developed further to include both shear and extensional stresses, from which numerical solutions for steady-state shelves are calculated. The results from these two models are then compared. It is found that shear stresses dominate the dynamics throughout the majority of the shelf, with adjustment regions at the upstream and downstream boundaries where extensional dynamics become important. Output from these models is also compared with geophysical data and it is observed that there is good agreement between several features of the thickness profiles and velocity fields.

In addition to the geophysical data, comparisons are made with fluid-mechanical laboratory experiments designed to simulate the flow of an ice shelf in a channel. The advantage of performing experiments of this kind is that parameters such as the fluid rheology can be varied, allowing for direct comparison with a range of parameters in the mathematical models. From these experiments, surface velocity fields and thickness profiles are collected, which are used to make comparisons with the models. Clear differences are observed in the velocity and strain-rate fields produced using fluids with different rheologies, for which there is qualitative agreement with the output from the mathematical models.