Steady plane flow of ice sheets over large-slope topography
✍ Scribed by L. W. Morland; A. Draghicescu
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 326 KB
- Volume
- 9
- Category
- Article
- ISSN
- 1180-4009
No coin nor oath required. For personal study only.
✦ Synopsis
The reduced model for a large ice sheet ¯ow is uniformly valid when the bed topography is ¯at or has slopes relative to the horizontal no greater than order e, where e 2 is a very small dimensionless viscosity based on the geometry and ¯ow parameters. Real beds will have much greater slopes, of order unity in places. Largescale numerical simulations of ice sheet evolution are currently based on the reduced model, and their validity when signi®cant basal topography is present, the common situation, is not certain. Numerical solution of the full slow viscous ¯ow equations on the unknown sheet domain, where the surface is stressfree and subject to a kinematic accumulation/melt condition, is much more dicult. No established algorithms exist at present. Here attention is focused on the most simple con®guration of steady plane ¯ow of an incompressible linearly viscous ¯uid, assuming isothermal conditions so that the temperature dependent rate factor is constant. It allows the application of complex potential representations for a solution of the full equations superposed on a ¯at bed reduced solution in order to satisfy non-slip conditions on a humped bed. A particular class of conformal mappings of a humped bed contour onto a ¯at bed result in boundary conditions which can be solved exactly by Cauchy integral methods to yield explicit integral representations for the potentials and related physical variables. Evaluation is necessarily numerical, but accurate. This method is applied to various humped contours with amplitude increasing from zero to determine when the reduced solution, ignoring the bed topography, starts to lose accuracy, and how far from the humped section this error persists. It is demonstrated that bed humps do in¯uence the velocity ®eld.