Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a...
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ftdatacite:10.48550/arxiv.1310.7998 2023-05-15T16:41:53+02:00 Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids Banik, Indranil Dauparas, Justas 2013 https://dx.doi.org/10.48550/arxiv.1310.7998 https://arxiv.org/abs/1310.7998 unknown arXiv https://dx.doi.org/10.4172/2572-3103.1000150 Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 CC-BY Fluid Dynamics physics.flu-dyn Geophysics physics.geo-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2013 ftdatacite https://doi.org/10.48550/arxiv.1310.7998 https://doi.org/10.4172/2572-3103.1000150 2022-04-01T13:17:41Z We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a simple generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain the equilibrium grounding line thickness using a simple computer model and to get an analytic approximation. For laterally confined shelves, we obtain an asymptotic theory valid for long shelves and define when this is. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was an aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx 3.8$ (similar to ice). Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). This strongly suggests that we have understood the dominant force balance in both types of ice shelf. In the real world, ice tongues are unlikely to rapidly disintegrate but can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. Prior to that point, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only oceanic conditions change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speedup of the sheet and a much smaller equilibrium grounding line thickness. Something similar may have occurred to the Larsen B ice shelf. : 37 pages, 16 figures, 6 tables. Accepted for publication in the open-access Journal of Oceanography and Marine Research in this form Text Ice Shelf Ice Shelves DataCite Metadata Store (German National Library of Science and Technology) |
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Open Polar |
collection |
DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
ftdatacite |
language |
unknown |
topic |
Fluid Dynamics physics.flu-dyn Geophysics physics.geo-ph FOS Physical sciences |
spellingShingle |
Fluid Dynamics physics.flu-dyn Geophysics physics.geo-ph FOS Physical sciences Banik, Indranil Dauparas, Justas Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
topic_facet |
Fluid Dynamics physics.flu-dyn Geophysics physics.geo-ph FOS Physical sciences |
description |
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a simple generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain the equilibrium grounding line thickness using a simple computer model and to get an analytic approximation. For laterally confined shelves, we obtain an asymptotic theory valid for long shelves and define when this is. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was an aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx 3.8$ (similar to ice). Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). This strongly suggests that we have understood the dominant force balance in both types of ice shelf. In the real world, ice tongues are unlikely to rapidly disintegrate but can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. Prior to that point, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only oceanic conditions change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speedup of the sheet and a much smaller equilibrium grounding line thickness. Something similar may have occurred to the Larsen B ice shelf. : 37 pages, 16 figures, 6 tables. Accepted for publication in the open-access Journal of Oceanography and Marine Research in this form |
format |
Text |
author |
Banik, Indranil Dauparas, Justas |
author_facet |
Banik, Indranil Dauparas, Justas |
author_sort |
Banik, Indranil |
title |
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
title_short |
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
title_full |
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
title_fullStr |
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
title_full_unstemmed |
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids |
title_sort |
ice shelves as floating channel flows of viscous power-law fluids |
publisher |
arXiv |
publishDate |
2013 |
url |
https://dx.doi.org/10.48550/arxiv.1310.7998 https://arxiv.org/abs/1310.7998 |
genre |
Ice Shelf Ice Shelves |
genre_facet |
Ice Shelf Ice Shelves |
op_relation |
https://dx.doi.org/10.4172/2572-3103.1000150 |
op_rights |
Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 |
op_rightsnorm |
CC-BY |
op_doi |
https://doi.org/10.48550/arxiv.1310.7998 https://doi.org/10.4172/2572-3103.1000150 |
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1766032360486207488 |