Basal Stress Concentrations Due to Abrupt Changes in Boundary Conditions: A Cause for High Till Concentration at the Bottom of a Glacier

Abstract

The existence of cold patches at the base of a glacier suggests that the sliding law will depend on these patches, which will essentially affect the viscosity constant. In a poly thermal glacier, such as a glacier which is cold in its lower part and temperate in its upper part, basal boundary conditions change from no-slip to viscous sliding. It is anticipated that the viscosity constant of this sliding law will depend on the distance from the transition line between cold and temperate ice.The mixed boundary conditions, namely no-slip where the ice is cold and viscous sliding where it is temperate, induce large stresses and velocity changes close to the transition line. In fact, it is shown that, for a Newtonian fluid and all investigated discontinuities of boundary data, square-root singularities of the stresses will develop at the transition line. Asymptotic expressions for the basal stresses are derived. The explicit forms of these asymptotic expansions depend on the form of the spatial dependence of the sliding law and, furthermore, on the numerical values of the viscosity coefficient. It is, moreover, argued that the stress concentrations are sufficiently pronounced to account for the removal of basal rock especially in regions of high cleavage concentrations, the details again depending upon the sliding coefficients.No mathematical details of the problem solved are presented as attention is focused on the physical processes.

Modeling the WorldView-derived seasonal velocity evolution of Kennicott Glacier, Alaska

“…The high spring sliding scenario (Scenario A) with two slippery patches, in which we impose the largest cross-glacier basal velocity gradients, produces the largest region of negative shear stresses. Previous authors have reported that this issue arises from a mathematical singularity at the transition from slip to no-slip (Hutter and Olunloyo, 1981;Schoof, 2004;Amundson and others, 2006). We evaluate the model sensitivity to employing abrupt transitions in basal boundary condition by prescribing a smoothly varying basal velocity.…”

“…We are aware that the abrupt transition from zero to high basal velocity, as prescribed above, is unrealistic and can induce a non-physical basal traction field (Hutter and Olunloyo, 1981;Schoof, 2004;Bueler and Brown, 2009). We analyze the shear stress field for each slip distribution case of each scenario and find the maximum basal shear stresses are generally within a plausible range of 100-150 kPa.…”

Glacial land forms indicative of a partly frozen bed

“…In the extending-flow zone, dispersal and thinning of the debris sheet will occur, possibly leaving the scarp as the main trace of the debris entrainment. In this context, it can be noted that Hutter and Olunloyo (1981) pointed out transition lines between frozen and thawed bed as sites of extreme stress concentrations.…”

Sedimentology, stratigraphy, and glacier dynamics, western scottish Highlands

“…Since Facies C has a silt and clay (rock flour) matrix and is very firm, it is interpreted as the product of bedrock erosion by plucking or micro-fracturing (sensu Hutter & Olunloyo, 1981).…”