Theory and Finite Element Analysis of Shallow Ice Shelves

• Main Author: Weis, Magnus
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: 2001
• Subjects: Antarctic; The Antarctic; Antarc*; Ice Sheet; Ice Shelf; Ice Shelves
• Online Access: http://tuprints.ulb.tu-darmstadt.de/171/; https://tuprints.ulb.tu-darmstadt.de/171/1/diss01.pdf; https://tuprints.ulb.tu-darmstadt.de/171/2/diss02.pdf; https://tuprints.ulb.tu-darmstadt.de/171/3/diss03.pdf

This thesis concerns the dynamics of ice shelves, which are large, floating ice masses that are adjacent to and fed by the Antarctic ice sheet. Starting from the approaches found in the literature for the derivation of simplified, zeroth order equations describing the dynamics of ice sheets, these methods are applied to ice shelves taking the dominant stresses into account. Two different layers of ice are distinguished: Meteoric ice that is built from precipitation that accumulates either on the ice shelf itself or the adjacent inland ice sheet and marine ice. The latter is built from phase transition processes at the ice-ocean interface or from the aggregation of ice particles called frazil ice ascending through the water column to the ice-shelf base. Thermodynamical boundary conditions for all the transition surfaces as well as kinematic boundary conditions for the free moving boundaries are formulated. By the use of constitutive equations, more generally valid balance equations are specialized to describe the flow of ice masses on long time scales. The equations derived are subjected to a scaling analysis and the aspect ratio, which is the ratio between a typical length scale and the typical ice thickness is identified as a small parameter that is used to subject the equations to a zeroth order perturbation expansion. Some of the equations are subjected to a vertical integration. Finally, this leads to a system of partial integro-differential equations that is completed by the boundary conditions as well as equations for the temperature, the age of the ice and evolution equations for the position of the free surfaces. In the second chapter, a finite element formulation is proposed for the previously derived equations approximating the mechanical aspects of ice-shelf dynamics. The equations are solved using an object oriented C++ class library specially designed for this purpose only. At first, the numerical model is applied to several academic ice-shelf setups and it is compared to an analytical solution ...