(untitled) (Archives of Mechanics - Test, 1997)
A review is given of the theory of cold ice sheets in the so-called shallow ice approximation, and a literature survey is performed of its application in ice sheet modelling of the large ice shields, such as Greenland, Antarctica and other, historical, ice sheets. As model applications, steady state and time-dependent computations are performed for the Greenland Ice Sheet using an ice sheet model on the basis of the 3-D shallow ice equations of a viscous, heat-conducting incompressible fluid. The interaction with the solid earth is through a heat-conducting homogeneous isotropic rigid solid subjected to geothermal heat. The climate driving is effected through a prescribed atmospheric surface temperature and accumulation rate function. Computations are performed for t he ice-thickness distribution to steady driving conditions when external and internal parameters are varied. It is shown that the sliding coefficient and the amplitude of the annual temperature variation are particularly critical. Finally, the evolution of the basal temperature distribution at Dye 3, Summit and Camp Century through idealized scenarios of the ice age(s) is computed; these computations show that the basal temperature regime depends critically on the thermal inertia of the bedrock and the magnitude of the ice fluidity. Our computations with various climate state scenarios demonstrate how well the model reproduces the measured flow data in Greenland and indicates how it must be extended to accomodate the polythermal structure of the ice and to include longitudinal stretching effects.