Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate
Abstract Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and poin...
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crcambridgeupr:10.1017/s0022143000015720 2024-03-03T08:45:28+00:00 Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate Hutter, Kolumban 1993 http://dx.doi.org/10.1017/s0022143000015720 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015720 en eng Cambridge University Press (CUP) Journal of Glaciology volume 39, issue 131, page 65-86 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1993 crcambridgeupr https://doi.org/10.1017/s0022143000015720 2024-02-08T08:41:37Z Abstract Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character. As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored. The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law. When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail. Article in Journal/Newspaper Ice Sheet Journal of Glaciology Cambridge University Press Journal of Glaciology 39 131 65 86 |
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English |
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Earth-Surface Processes |
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Earth-Surface Processes Hutter, Kolumban Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
topic_facet |
Earth-Surface Processes |
description |
Abstract Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character. As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored. The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law. When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail. |
format |
Article in Journal/Newspaper |
author |
Hutter, Kolumban |
author_facet |
Hutter, Kolumban |
author_sort |
Hutter, Kolumban |
title |
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
title_short |
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
title_full |
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
title_fullStr |
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
title_full_unstemmed |
Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
title_sort |
thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate |
publisher |
Cambridge University Press (CUP) |
publishDate |
1993 |
url |
http://dx.doi.org/10.1017/s0022143000015720 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015720 |
genre |
Ice Sheet Journal of Glaciology |
genre_facet |
Ice Sheet Journal of Glaciology |
op_source |
Journal of Glaciology volume 39, issue 131, page 65-86 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000015720 |
container_title |
Journal of Glaciology |
container_volume |
39 |
container_issue |
131 |
container_start_page |
65 |
op_container_end_page |
86 |
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1792501024997507072 |