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Abstract

Based on the physical processes governing the motion and dynamics of poly-thermal ice sheets, we distinguish two regions; the cold region, where the ice temperature is below the melting point, and the temperate region, where the ice temperature is exactly equal to the melting point, leading to the presence of a water fraction. This work focuses on the analysis and description of the temperate zone on the basis of rational thermo-dynamics of reacting mixtures. The balance laws for the ice-water mixture, that is the mass balance, balance of linear and angular momenta, energy and entropy, are discussed. A physical model for a polythermal ice sheet is then established, including appropriate boundary and transition conditions. The resulting formulation is convenient for numerical implementation. Numerical examples are carried out for a stationary 2-D case and the results of the present and traditional formulations are compared.