Ice Flow Over Bedrock Perturbations

Abstract

The use of well known simple periodic solutions of the two-dimensional biharmonic stress equation for studying the flow over undulations of an ice mass of small surface slope is examined. The model considered is one in which most of the shear (deformation or. sliding) takes place near the base and the upper part moves largely as a block, with longitudinal strain-rates varying linearly with the longitudinal stress deviations. For bedrock perturbations of a given wavelength the steady-state surface shape consists of similar waves but out of phase by ½π, such that the steepest slope occurs over the highest bedrock; and the amplitude is reduced by a “damping factor”, depending on the speed, viscosity, ice thickness and wavelength.Minimum damping occurs for λ_m ≈ 3.3 times the ice thickness, while waves much longer or much shorter than this are almost completely damped out. The energy dissipation and the resistance to the ice flow is also a maximum for an undulation scale of several times the ice thickness, whereas the effects of small basal irregularities die out exponentially with distance into the ice, and only have an effect in so far as the average basal stress is related to the average surface slope. As a result of this a revision of present glacier sliding theories becomes possible.Various predictions of the theory have been confirmed from spectral analysis of surface and bedrock profiles of ice caps.