NEAR-SURFACE FLOW IN GLACIERS OBEYING GLEN'S LAW

• Published in: The Quarterly Journal of Mechanics and Applied Mathematics
• Main Authors: JOHNSON, ROBERT E., McMEEKING, ROBERT M.
• Format: Text
• Language: English
• Published: Oxford University Press 1984
• Subjects: Articles; Ice Sheet
• Online Access: http://qjmam.oxfordjournals.org/cgi/content/short/37/2/273; https://doi.org/10.1093/qjmam/37.2.273

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 δ1/n where δ = h 0 /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.