First-Order Stresses and Deformations in Glaciers and Ice Sheets
Abstract In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatme...
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Language: | English |
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Cambridge University Press (CUP)
1981
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Online Access: | http://dx.doi.org/10.1017/s0022143000015379 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015379 |
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crcambridgeupr:10.1017/s0022143000015379 2024-03-03T08:46:09+00:00 First-Order Stresses and Deformations in Glaciers and Ice Sheets Hutter, Kolumban Legerer, Fritz Spring, Ulrich 1981 http://dx.doi.org/10.1017/s0022143000015379 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015379 en eng Cambridge University Press (CUP) Journal of Glaciology volume 27, issue 96, page 227-270 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1981 crcambridgeupr https://doi.org/10.1017/s0022143000015379 2024-02-08T08:40:23Z Abstract In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatment of the accumulation–ablation mechanism. It is then shown how the emerging set of non-linear equations for the established boundary-value problem can be separated into a system covering steady-state problems on the one hand, and transient, time-dependent processes on the other hand. This separation is performed under the assumption that steady-state stresses are larger than the corresponding transient counterparts, suggesting a linearization of the transient equations with regard to the stresses. The steady-state equations are then analysed for the special case of an infinitely long, nearly parallel-sided slab. With the assumption that bottom undulations are small as compared to the glacier thickness it is shown that the original non-linear boundary-value problem can be decomposed into an infinite hierarchy of boundary-value problems defined on the simpler domain of the exactly parallel-sided slab, all of which are linear except for the lowest order one. Since its solution is readily available, the determination of the velocities and stresses due to bedrock protuberances is basically a linear problem, even though the constitutive response may be non-linear. Assuming harmonic bedrock undulations we show for a Navier–Stokes fluid that the transfer of the bedrock undulations to the surface strongly depends on the mean inclination of the slab, but, more importantly, does now show a maximum when plotted as a function of wavelength λ. This result is contradictory to the corresponding results of Budd (1970[a]) and implies serious drawbacks to his calculations of longitudinal stresses and strain-rates in his subsequent article (Budd, 1970[b]). Yet, it is not true that for maximal transfer of bottom protuberances to the ... Article in Journal/Newspaper Journal of Glaciology Cambridge University Press Journal of Glaciology 27 96 227 270 |
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Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes Hutter, Kolumban Legerer, Fritz Spring, Ulrich First-Order Stresses and Deformations in Glaciers and Ice Sheets |
topic_facet |
Earth-Surface Processes |
description |
Abstract In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatment of the accumulation–ablation mechanism. It is then shown how the emerging set of non-linear equations for the established boundary-value problem can be separated into a system covering steady-state problems on the one hand, and transient, time-dependent processes on the other hand. This separation is performed under the assumption that steady-state stresses are larger than the corresponding transient counterparts, suggesting a linearization of the transient equations with regard to the stresses. The steady-state equations are then analysed for the special case of an infinitely long, nearly parallel-sided slab. With the assumption that bottom undulations are small as compared to the glacier thickness it is shown that the original non-linear boundary-value problem can be decomposed into an infinite hierarchy of boundary-value problems defined on the simpler domain of the exactly parallel-sided slab, all of which are linear except for the lowest order one. Since its solution is readily available, the determination of the velocities and stresses due to bedrock protuberances is basically a linear problem, even though the constitutive response may be non-linear. Assuming harmonic bedrock undulations we show for a Navier–Stokes fluid that the transfer of the bedrock undulations to the surface strongly depends on the mean inclination of the slab, but, more importantly, does now show a maximum when plotted as a function of wavelength λ. This result is contradictory to the corresponding results of Budd (1970[a]) and implies serious drawbacks to his calculations of longitudinal stresses and strain-rates in his subsequent article (Budd, 1970[b]). Yet, it is not true that for maximal transfer of bottom protuberances to the ... |
format |
Article in Journal/Newspaper |
author |
Hutter, Kolumban Legerer, Fritz Spring, Ulrich |
author_facet |
Hutter, Kolumban Legerer, Fritz Spring, Ulrich |
author_sort |
Hutter, Kolumban |
title |
First-Order Stresses and Deformations in Glaciers and Ice Sheets |
title_short |
First-Order Stresses and Deformations in Glaciers and Ice Sheets |
title_full |
First-Order Stresses and Deformations in Glaciers and Ice Sheets |
title_fullStr |
First-Order Stresses and Deformations in Glaciers and Ice Sheets |
title_full_unstemmed |
First-Order Stresses and Deformations in Glaciers and Ice Sheets |
title_sort |
first-order stresses and deformations in glaciers and ice sheets |
publisher |
Cambridge University Press (CUP) |
publishDate |
1981 |
url |
http://dx.doi.org/10.1017/s0022143000015379 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015379 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 27, issue 96, page 227-270 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000015379 |
container_title |
Journal of Glaciology |
container_volume |
27 |
container_issue |
96 |
container_start_page |
227 |
op_container_end_page |
270 |
_version_ |
1792502130949488640 |