Shear margins in glaciers and ice sheets

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Abstract
Analytical and numerical techniques are used to examine the flow response of a sloped slab of power-law fluid (powern) subjected to basal boundary conditions that vary 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 asr, 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 greater width of the flow. In units of ice thicknessH, the spatial scale of spreading is proportional to a single dimensionless numberRn≡ (r/n+ 1)1/n+1derived fromnandr. 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 toRn. For an ice stream caused by a band of low slip resistance with a half-width ofw H, the margins influence velocity and stress in the central part of the band depending onRnin comparison tow. Three regimes can be identified, which forn= 3 are quantified as follows: lowrdefined asR3< 0.1w, for which the central flow is essentially unaffected by the margins and the driving stress is supported entire by by basal drag; highrdefined asR3> 1w, for which the boundary layers from both sides bridge across the full flow width and the driving stress in the center is supported almost entirely by side drag; intermediater, 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 (≈R3) would require localized softening of the ice to explain the concentration of deformation at a shorter scale.