Abstract
Abstract In the standard solution for the stresses in a glacier or ice sheet obeying Glen’s law, the down-slope component of the weight is supported by the basal shear stress, and the longitudinal deviatoric stress is second order. However, it has been found necessary to account for the longitudinal stress gradient when relating surface to bed topography with empirical data. In addition, during rapid stretching of the glacier, perhaps during a surge, the longitudinal stress gradient becomes comparable to or larger than the shear stress, and the standard solution is not entirely valid. In this paper, we consider the analysis of the stresses and strain-rates in a glacier when the longitudinal deviatoric stresses are comparable to the basal shear stresses. In some circumstances the down-slope component of weight is not borne completely by basal shear stress to leading order and some of the weight is shifted to the longitudinal deviatoric stress gradient. This case has also been examined. The results are used to obtain expressions for basal shear stress in terms of glacier thickness, slope, surface strain-rate gradient, and ice properties.
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