Plasticity Solution for a Glacier Snout

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Abstract
The flow near the end of a glacier in a steady state is investigated by using a theoretical model: a plastic–rigid material with a constant flow stress resting on a rough horizontal bed. Starting from an appropriately chosen slip-line far from the end, the slip-line field is constructed numerically and continued to the end of the glacier. The field rapidly settles down to a form independent of the precise starting conditions. In the region of small surface slope it agrees with the approximate analytical solution reported earlier (Nye, 1951). To avoid a breakdown in the method it is found necessary to modify the bed by a trivial amount over the final 3 m. In practice the ice can lose contact with the bed very near the end, and the effect of this on the solution is discussed. The velocity field is computed for a uniform ablation-rate. Other distributions of ablation-rate could be accommodated, but there appears to be a critical gradient of ablation-rate beyond which the slip-line field fails.

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