Asymptotic analysis of flow near a glacier terminus

The non-linearly viscous ice flow in the vicinity of a glacier terminus, an observation region, depends crucially on the upstream flow as well as on the local surface and bed conditions. The former requires a likely complex solution of the balance laws and boundary conditions for the complete glacier. However, if the profile and downstream surface tangential velocity in the observation region are measured at an observation time t = 0, and a two-dimensional flow approximation is satisfactory, the complete stress and velocity fields satisfying local reduced model equations in the observation region at time t = 0 can be determined by asymptotic expansions in upstream distance from the (moving) terminus. Thus the full strain-rate and stress tensors are determined without prescribing the basal conditions. The terminus velocity is determined in terms of the net accumulation or melt flux and surface velocity at the terminus, with bounds for advance or retreat. The analysis and illustration are presented for a plane flow approximation.