Modelling glacial erosional landform development
Glacial erosional systems exhibit a complex, highly scaledependent phenomenology. Some aspects of modelling the development of glacial erosional landforms in response to glacial erosional processes acting over a wide range of scales are considered. The physics of ice at the glacier sole is discussed. A simple ice-water mixture theory is proposed. A method for finding the solution of the equations of motion of ice at the glacier sole based on the finite element velocities-pressure formulation is shown, which includes novel formulations for the sliding boundary condition, compression of ice and flow of water between ice and bedrock. These finite element formulations are used to simulate flows at the ice-rock interface. The use of the Laplace equation in simulating uni-axial flow is also considered, and further simulations are carried out using this equation. The results from these finite element simulations are used to consider erosional processes occurring at the glacier bed. The processes of abrasion are considered, and previous models are shown to be physically inconsistent. Cavitation, transiency and heterogeneity are shown to have an effect on clast-bed contact forces, and the local viscosity of ice is identified as being a further controlling variable on abrasion. These results are used to consider the likely development of hummocks of bedrock. A mass-balance analysis of basal debris is carried out and shown to have an important effect on erosional patterns. The equations describing the movement of a surface normal to itself are considered. Various solution techniques for these equations are tested, and requirements for the persistence of form under lowering are given. The modelling strategy used in this thesis is a nested hierarchy, with the various hierarchical levels corresponding to different scales. The effect of this hierarchisation on the modelling is discussed with respect to the generic properties of the systems, explanation and testability.