Marine ice sheet dynamics. Part 2. A Stokes flow contact problem
We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constr...
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Cambridge University Press (CUP)
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Online Access: | http://dx.doi.org/10.1017/jfm.2011.129 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112011001297 |
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crcambridgeupr:10.1017/jfm.2011.129 2024-03-03T08:45:25+00:00 Marine ice sheet dynamics. Part 2. A Stokes flow contact problem SCHOOF, CHRISTIAN 2011 http://dx.doi.org/10.1017/jfm.2011.129 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112011001297 en eng Cambridge University Press (CUP) https://www.cambridge.org/core/terms Journal of Fluid Mechanics volume 679, page 122-155 ISSN 0022-1120 1469-7645 Mechanical Engineering Mechanics of Materials Condensed Matter Physics journal-article 2011 crcambridgeupr https://doi.org/10.1017/jfm.2011.129 2024-02-08T08:31:52Z We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line. Article in Journal/Newspaper Ice Sheet Ice Shelf Cambridge University Press Journal of Fluid Mechanics 679 122 155 |
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Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
spellingShingle |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics SCHOOF, CHRISTIAN Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
topic_facet |
Mechanical Engineering Mechanics of Materials Condensed Matter Physics |
description |
We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line. |
format |
Article in Journal/Newspaper |
author |
SCHOOF, CHRISTIAN |
author_facet |
SCHOOF, CHRISTIAN |
author_sort |
SCHOOF, CHRISTIAN |
title |
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
title_short |
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
title_full |
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
title_fullStr |
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
title_full_unstemmed |
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem |
title_sort |
marine ice sheet dynamics. part 2. a stokes flow contact problem |
publisher |
Cambridge University Press (CUP) |
publishDate |
2011 |
url |
http://dx.doi.org/10.1017/jfm.2011.129 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112011001297 |
genre |
Ice Sheet Ice Shelf |
genre_facet |
Ice Sheet Ice Shelf |
op_source |
Journal of Fluid Mechanics volume 679, page 122-155 ISSN 0022-1120 1469-7645 |
op_rights |
https://www.cambridge.org/core/terms |
op_doi |
https://doi.org/10.1017/jfm.2011.129 |
container_title |
Journal of Fluid Mechanics |
container_volume |
679 |
container_start_page |
122 |
op_container_end_page |
155 |
_version_ |
1792500982869917696 |