On the transport of moisture in polythermal glaciers

Abstract

We reconsider the problem of formulation of a model for polythermal glaciers, focussing attention in particular on the temperate zone where ice and water can coexist at the melting temperature. The energy equation for the ice-water mixture in this zone introduces a moisture flux, and a constitutive law for this flux is required. By analogy with the flow through a porous medium, we use Darcy's law (i.e. the second momentum equation of a two-phase flow model with “porous” geometry), and then require a mechanical constitutive relation relating the water pressure p _w to the average ice pressure p _i . Experience in two phase flows suggests that p _w =p _i may be problematical, and experience in soil mechanics suggests it is inaccurate. A constitutive relation is therefore presented based on work of Nye (1976), and its effect on the well-posedness of the model is examined. Considerations of the sort presented here have clear relevance in the formulation of similar problems in other geophysical situations, notably mantle convection.