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Near-surface flow in glaciers obeying Glen’s law. (English) Zbl 0616.76007
In determining the gravity-driven flow of a glacier or ice sheet which obeys Glen’s flow law, previous methods have predicted infinite longitudinal stress at the glacier’s surface. This physically unacceptable occurrence is due to a break-down in the mathematical methods used to obtain the solution. Using the method of matched asymptotic expansions, the solution valid in the near-surface region of a steady-state glacier is determined. The size of the near-surface or boundary-layer region is found to be of order delta 1n, where $$delta=h0/L$$ is the assumed small ratio of the characteristic thickness and length of the ice sheet and n is the exponent in Glen’s power law. The solution is obtained for ice sheets on both a steep and gentle base slope. The stress field in the near-surface region is obtained and we find that the boundary layer does not significantly affect the surface velocities or the glacier profile.

##### MSC:
 76A05 Non-Newtonian fluids 86A60 Geological problems
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