Steady Motion of Ice Sheets
Abstract Steady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, an...
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Cambridge University Press (CUP)
1980
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Online Access: | http://dx.doi.org/10.1017/s0022143000010467 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000010467 |
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crcambridgeupr:10.1017/s0022143000010467 2024-03-03T08:45:26+00:00 Steady Motion of Ice Sheets Morland, L. W. Johnson, I. R. 1980 http://dx.doi.org/10.1017/s0022143000010467 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000010467 en eng Cambridge University Press (CUP) Journal of Glaciology volume 25, issue 92, page 229-246 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1980 crcambridgeupr https://doi.org/10.1017/s0022143000010467 2024-02-08T08:36:10Z Abstract Steady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε ( ν ) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions. Article in Journal/Newspaper Ice Sheet Journal of Glaciology Cambridge University Press Colbeck ENVELOPE(-158.017,-158.017,-77.117,-77.117) Journal of Glaciology 25 92 229 246 |
institution |
Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes Morland, L. W. Johnson, I. R. Steady Motion of Ice Sheets |
topic_facet |
Earth-Surface Processes |
description |
Abstract Steady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε ( ν ) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions. |
format |
Article in Journal/Newspaper |
author |
Morland, L. W. Johnson, I. R. |
author_facet |
Morland, L. W. Johnson, I. R. |
author_sort |
Morland, L. W. |
title |
Steady Motion of Ice Sheets |
title_short |
Steady Motion of Ice Sheets |
title_full |
Steady Motion of Ice Sheets |
title_fullStr |
Steady Motion of Ice Sheets |
title_full_unstemmed |
Steady Motion of Ice Sheets |
title_sort |
steady motion of ice sheets |
publisher |
Cambridge University Press (CUP) |
publishDate |
1980 |
url |
http://dx.doi.org/10.1017/s0022143000010467 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000010467 |
long_lat |
ENVELOPE(-158.017,-158.017,-77.117,-77.117) |
geographic |
Colbeck |
geographic_facet |
Colbeck |
genre |
Ice Sheet Journal of Glaciology |
genre_facet |
Ice Sheet Journal of Glaciology |
op_source |
Journal of Glaciology volume 25, issue 92, page 229-246 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000010467 |
container_title |
Journal of Glaciology |
container_volume |
25 |
container_issue |
92 |
container_start_page |
229 |
op_container_end_page |
246 |
_version_ |
1792500985555320832 |