Calculations of Velocity and Temperature in a Polar Glacier using the Finite-Element Method

• Published in: Journal of Glaciology
• Main Authors: Hooke, Roger LeB., Raymond, Charles F., Hotchkiss, Richard L., Gustafson, Robert J.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1979
• Subjects: Earth-Surface Processes; Barnes Ice Cap; Ice cap; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000014696; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000014696

Abstract Numerical methods based on quadrilateral finite elements have been developed for calculating distributions of velocity and temperature in polar ice sheets in which horizontal gradients transverse to the flow direction are negligible. The calculation of the velocity field is based on a variational principle equivalent to the differential equations governing incompressible creeping flow. Glen’s flow law relating effective strain-rate ε ̇ and shear stress τ by ε ̇ = ( τ/B ) n is assumed, with the flow law parameter B varying from element to element depending on temperature and structure. As boundary conditions, stress may be specified on part of the boundary, in practice usually the upper free surface, and velocity on the rest. For calculation of the steady-state temperature distribution we use Galerkin’s method to develop an integral condition from the differential equations. The calculation includes all contributions from vertical and horizontal conduction and advection and from internal heat generation. Imposed boundary conditions are the temperature distribution on the upper surface and the heat flux elsewhere For certain simple geometries, the flow calculation has been tested against the analytical solution of Nye (1957), and the temperature calculation against analytical solutions of Robin (1955) and Budd (1969), with excellent results. The programs have been used to calculate velocity and temperature distributions in parts of the Barnes Ice Cap where extensive surface and bore-hole surveys provide information on actual values. The predicted velocities are in good agreement with measured velocities if the flow-law parameter B is assumed to decrease down-glacier from the divide to a point about 2 km above the equilibrium line, and then remain constant nearly to the margin. These variations are consistent with observed and inferred changes in fabric from fine ice with random c -axis orientations to coarser ice with single- or multiple-maximum fabrics. In the wedge of fine-grained deformed superimposed ...