Surging glaciers II: mathematically exact two-dimensional stress tensor fields

Abstract

The linear boundary value problem for the stress tensor field $${\mathbf {S}}$$ in a glacier is considered. This problem is determined by the balance of forces and of torques inside the glacier and by vanishing stresses at the free surface. A mathematically exact two-dimensional general solution $${\mathbf {S}}$$ of this problem is developed, depending on its arbitrarily prescribed deviatoric longitudinal stress component. We complement a paper ‘Surging Glaciers I’ (Halfar in Acta Mech, 2020) and detail results spelled out there. Furthermore, an alternative exact expression of $${\mathbf {S}}$$ is outlined, depending on the arbitrarily prescribed longitudinal stress component.