SHEAR MARGINS IN GLACIERS AND ICE SHEETS

Analytical and numerical techniques are used to examine the flow respo nse of a sloped slab of power-law fluid (power n) subjected to basal b oundary conditions that very spatially across the flow direction, as f or example near an ice-stream margin with planar basal topography. The primary assumption is that basal shear stress is proportional to the basal speed times a spatially variable slip resistance. The ratio of m ean basal speed to the speed originating from shearing through the thi ckness, denoted as r, gives a measure of how slippery the bed is. The principal conclusion is that a localized disturbance in slip resistanc e affects the basal stress and speed in a zone spread over a grater wi dth of the flow. In units of ice thickness H, the spatial scale of spr eading is proportional to a single dimensionless number R(n) = (r/n 1)(1/n+1) derived from n and r. The consequence for a shear zone above a sharp jump in slip resistance is that the shearing is spread out ov er a boundary layer with a width proportional to R(n). For an ice stre am caused by a band of low slip resistance with half-width of wH, the margins influence velocity and stress in the central part of the band depending on R(n) in comparison to w. Three regimes can be identified, which for n = 3 are quantified as follows: low r defined as R(3) < 0. 1w, for which the central flow is essentially unaffected by the margin s and the driving stress is supported entirely by basal drag; intermed iate r, for which the driving stress in the center is supported by a c ombination of basal and side drag. Shear zones that are narrower than predicted on the basis of this theory (approximate to R(3)) would requ ire localized softening of the ice to explain the concentration of def ormation at a shorter scale.