A continuum-mechanical formulation for shallow polythermal ice sheets
This paper is concerned with a new theoretical approach to model grounded ice sheets in three dimensions. These are considered as polythermal, i.e., there will be regions with temperatures below the pressure melting point ("cold ice") and regions with temperatures exactly at the pressure m...
Published in: | Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences |
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fthokunivhus:oai:eprints.lib.hokudai.ac.jp:2115/34856 2023-05-15T16:28:00+02:00 A continuum-mechanical formulation for shallow polythermal ice sheets Greve, Ralf http://hdl.handle.net/2115/34856 https://doi.org/10.1098/rsta.1997.0050 eng eng Royal Society http://royalsociety.metapress.com/content/102021 http://hdl.handle.net/2115/34856 Philosophical Transactions of The Royal Society. A, Mathematical Physical and Engineering Sciences, 355(1726): 921-974 http://dx.doi.org/10.1098/rsta.1997.0050 Ice sheet Polythermal Continuum mechanics Shallow ice approximation Greenland 452 article (author version) fthokunivhus https://doi.org/10.1098/rsta.1997.0050 2022-11-18T01:01:39Z This paper is concerned with a new theoretical approach to model grounded ice sheets in three dimensions. These are considered as polythermal, i.e., there will be regions with temperatures below the pressure melting point ("cold ice") and regions with temperatures exactly at the pressure melting point ("temperate ice"). In the latter, small quantities of water may occur. Based on previous approaches, an improved theory of polythermal ice sheets is developed, which is founded on continuum-thermodynamic balance relations and jump conditions for mass, momentum and energy. The rheological behaviour is assumed to be that of an incompressible, nonlinear viscous and heat conducting fluid; because of the dependence of viscosity on temperature and on water content, the problem is thermo-mechanically coupled. After presenting analytic solutions for a simple geometry (ice sheet of uniform depth), the theory is subjected to a scaling procedure with the assumptions of a small aspect ratio (ratio between typical vertical dimension and typical horizontal dimension) and a small Froude number. This leads to the introduction of the polythermal shallow-ice approximation (SIA) equations. Finally, as an application of the model to a real problem, a numerically computed steady-state solution for the Greenland Ice Sheet under present climate conditions is presented and compared with the real ice sheet. Article in Journal/Newspaper Greenland Ice Sheet Hokkaido University Collection of Scholarly and Academic Papers (HUSCAP) Greenland Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 355 1726 921 974 |
institution |
Open Polar |
collection |
Hokkaido University Collection of Scholarly and Academic Papers (HUSCAP) |
op_collection_id |
fthokunivhus |
language |
English |
topic |
Ice sheet Polythermal Continuum mechanics Shallow ice approximation Greenland 452 |
spellingShingle |
Ice sheet Polythermal Continuum mechanics Shallow ice approximation Greenland 452 Greve, Ralf A continuum-mechanical formulation for shallow polythermal ice sheets |
topic_facet |
Ice sheet Polythermal Continuum mechanics Shallow ice approximation Greenland 452 |
description |
This paper is concerned with a new theoretical approach to model grounded ice sheets in three dimensions. These are considered as polythermal, i.e., there will be regions with temperatures below the pressure melting point ("cold ice") and regions with temperatures exactly at the pressure melting point ("temperate ice"). In the latter, small quantities of water may occur. Based on previous approaches, an improved theory of polythermal ice sheets is developed, which is founded on continuum-thermodynamic balance relations and jump conditions for mass, momentum and energy. The rheological behaviour is assumed to be that of an incompressible, nonlinear viscous and heat conducting fluid; because of the dependence of viscosity on temperature and on water content, the problem is thermo-mechanically coupled. After presenting analytic solutions for a simple geometry (ice sheet of uniform depth), the theory is subjected to a scaling procedure with the assumptions of a small aspect ratio (ratio between typical vertical dimension and typical horizontal dimension) and a small Froude number. This leads to the introduction of the polythermal shallow-ice approximation (SIA) equations. Finally, as an application of the model to a real problem, a numerically computed steady-state solution for the Greenland Ice Sheet under present climate conditions is presented and compared with the real ice sheet. |
format |
Article in Journal/Newspaper |
author |
Greve, Ralf |
author_facet |
Greve, Ralf |
author_sort |
Greve, Ralf |
title |
A continuum-mechanical formulation for shallow polythermal ice sheets |
title_short |
A continuum-mechanical formulation for shallow polythermal ice sheets |
title_full |
A continuum-mechanical formulation for shallow polythermal ice sheets |
title_fullStr |
A continuum-mechanical formulation for shallow polythermal ice sheets |
title_full_unstemmed |
A continuum-mechanical formulation for shallow polythermal ice sheets |
title_sort |
continuum-mechanical formulation for shallow polythermal ice sheets |
publisher |
Royal Society |
url |
http://hdl.handle.net/2115/34856 https://doi.org/10.1098/rsta.1997.0050 |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
Greenland Ice Sheet |
genre_facet |
Greenland Ice Sheet |
op_relation |
http://royalsociety.metapress.com/content/102021 http://hdl.handle.net/2115/34856 Philosophical Transactions of The Royal Society. A, Mathematical Physical and Engineering Sciences, 355(1726): 921-974 http://dx.doi.org/10.1098/rsta.1997.0050 |
op_doi |
https://doi.org/10.1098/rsta.1997.0050 |
container_title |
Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences |
container_volume |
355 |
container_issue |
1726 |
container_start_page |
921 |
op_container_end_page |
974 |
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1766017605241405440 |