Abstract
AbstractThe 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.
Highlights
Nye (2015) constructed an approximate plane flow velocity distribution near the glacier terminus consistent with Glen (1961)’s measured profile and surface velocity distributions on Austerdalsbreen in 1958 and 1959
A plane flow local reduced model solution is constructed for the terminus vicinity – an observation region – assuming a known surface profile and known surface tangential velocity at the observation time t = 0; a snapshot of the flow
The local reduced model is a set of leading order relations in a small parameter e, which neglects terms of order e compared with unity. e is a coordinate and velocity scaling factor which is determined by the small dimensionless viscosity ν incorporating the observation region thickness magnitude d0.The validity of the local reduced model requires that the slopes of the bed undulations relative to the mean bed plane are not greater than e in magnitude
Summary
Nye (2015) constructed an approximate plane flow velocity distribution near the glacier terminus consistent with Glen (1961)’s measured profile and surface velocity distributions on Austerdalsbreen in 1958 and 1959 He adopts the conventional viscous power law for the ice, assumed to be close to melting so the temperature-dependent rate factor is constant (unity). E is a coordinate and velocity scaling factor which is determined by the small dimensionless viscosity ν incorporating the observation region thickness magnitude d0.The validity of the local reduced model requires that the slopes of the bed undulations relative to the mean bed plane are not greater than e in magnitude. The validity of the simplification and its consequences are noted
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