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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Published in:Journal of Glaciology
Main Author: Hutter, Kolumban
Format: Article in Journal/Newspaper
Language:English
Published: Cambridge University Press (CUP) 1993
Subjects:
Online Access:http://dx.doi.org/10.1017/s0022143000015720
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000015720
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spelling 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
institution Open Polar
collection Cambridge University Press
op_collection_id crcambridgeupr
language English
topic Earth-Surface Processes
spellingShingle 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
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