A mathematical model of polythermal glaciers and ice sheets

Abstract

A mathematical model of the flow and temperature distribution of polythermal glaciers or ice sheets is deduced. Cold ice is treated as a non-linear viscous heat conducting fluid, while temperate ice is regarded as a binary mixture of ice and water. The simplest mixture concept with two balance laws of mass but only one balance law of momentum and energy is proposed. The field equations for the ice and water content and the boundary conditions which must hold at the free surface, at the ice-water interface, at the cold-temperature transition surface and at the rock-bed are deduced. In particular it is shown that an earlier formulation of polythermal ice due to Fowler and Larson (1978) is inconsistent. No boundary value problems are solved as the emphasis is on the physical motivation and justification of the principles.