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.