A new fully three-dimensional numerical model for ice dynamics

The problem of describing ice dynamics has been faced by many researchers; in this paper a fully three-dimensional model for ice dynamics is presented and tested. Using an approach followed by other researchers, ice is considered a non-linear incompressible viscous fluid so that a fluid-dynamic approach can be used. The model is based on the full three-dimensional Stokes equations for the description of pressure and velocity fields, on the Saint-Venant equation for the description of the free-surface time evolution and on a constitutive law derived from Glen's law for the description of ice viscosity. The model computes the complete pressure field by considering both the hydrostatic and hydrodynamic pressure components; it is time-evolutive and uses high-order numerical approximation for equations and boundary conditions. Moreover it can deal with both constant and variable viscosity. Three theoretical tests and two applications to Priestley Glacier, Antarctica, are presented in order to evaluate the performance of the model and to investigate important phenomena of ice dynamics such as the influence of viscosity on pressure and velocity fields, basal sliding and flow over perturbed bedrocks. All these applications demonstrate the importance of treating the complete pressure and stress fields.