Shear margins in glaciers and ice sheets

Analytical and numerical techniques are used to examine the flow response of a sloped slab of power-law fluid (power n) subjected to basal boundary conditions that very spatially across the flow direction, as for 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 mean basal speed to the speed originating from shearing through the thickness, denoted as r, gives a measure of how slippery the bed is. The principal conclusion is that a localized disturbance in slip resistance affects the basal stress and speed in a zone spread over a grater width of the flow. In units of ice thickness H, the spatial scale of spreading 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 over a boundary layer with a width proportional to R(n). For an ice stream 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 margins and the driving stress is supported entirely by basal drag; intermediate r, for which the driving stress in the center is supported by a combination of basal and side drag. Shear zones that are narrower than predicted on the basis of this theory (approximate to R(3)) would require localized softening of the ice to explain the concentration of deformation at a shorter scale.