Thermomechanisches Verhalten polythermer Eisschilde - Theorie, Analytik, Numerik
This thesis is concerned with the theoretical, analytical and numerical modelling of grounded ice sheets in three dimensions. These are considered as polythermal, i.e., it is accounted for the fact that there may be regions with temperatures below the pressure melting point ("cold ice") as well as regions with temperatures exactly on the pressure melting point ("temperate ice"). In the latter, small quantities of water may occur in addition.
Based on previous approaches, an improved theory of polythermal ice sheets is developed, which is founded on continuum-thermodynamic balance relations and jump conditions for mass, momentum and energy. The rheologic behaviour is hereby assumed to follow an incompressible, nonlinear viscous and heat conducting fluid; because of the dependence of viscosity on temperature and water content the problem is thermo-mechanically coupled. After giving analytic solutions for a simple geometry (parallel-sided ice slab), the theory is subjected to a scaling procedure with the assumptions of a small aspect ratio (ratio between typical vertical dimension and typical horizontal dimension) and a small Froude number. This leads to the introduction of the polythermal shallow-ice approximation (SIA) equations.
Subsequently, a numerical solution scheme for these equations is given, making use of a finite difference approach. In the vertical, the model domain is mapped onto the unit interval in order to make the implementation of boundary conditions easier. Using the computer code developed from this, model runs for two different problems are carried out. First, the EISMINT ice sheet is dealt with, consisting of a flat square-shaped bedrock subject to spatially uniform snowfall. Second, simulations for the Greenland ice sheet are discussed, that were carried out for both steady state conditions and time-dependent scenarios, namely sinusoidal variations, a realistic climate history deduced from ice core reconstruction, and increased temperatures due to intensified greenhouse warming.
Doctoral thesis, Department of Mechanics, Darmstadt University of Technology,
Germany, 226 pp. (1995).