Similitude of ice dynamics against scaling of geometry and physical parameters
The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling o...
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2016
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ftdoajarticles:oai:doaj.org/article:e50c97b29c7e492e89eceb71b9013360 2023-05-15T16:40:40+02:00 Similitude of ice dynamics against scaling of geometry and physical parameters J. Feldmann A. Levermann 2016-08-01T00:00:00Z https://doi.org/10.5194/tc-10-1753-2016 https://doaj.org/article/e50c97b29c7e492e89eceb71b9013360 EN eng Copernicus Publications http://www.the-cryosphere.net/10/1753/2016/tc-10-1753-2016.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 1994-0416 1994-0424 doi:10.5194/tc-10-1753-2016 https://doaj.org/article/e50c97b29c7e492e89eceb71b9013360 The Cryosphere, Vol 10, Iss 4, Pp 1753-1769 (2016) Environmental sciences GE1-350 Geology QE1-996.5 article 2016 ftdoajarticles https://doi.org/10.5194/tc-10-1753-2016 2022-12-31T13:08:40Z The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations. Article in Journal/Newspaper Ice Sheet The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 10 4 1753 1769 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
spellingShingle |
Environmental sciences GE1-350 Geology QE1-996.5 J. Feldmann A. Levermann Similitude of ice dynamics against scaling of geometry and physical parameters |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations. |
format |
Article in Journal/Newspaper |
author |
J. Feldmann A. Levermann |
author_facet |
J. Feldmann A. Levermann |
author_sort |
J. Feldmann |
title |
Similitude of ice dynamics against scaling of geometry and physical parameters |
title_short |
Similitude of ice dynamics against scaling of geometry and physical parameters |
title_full |
Similitude of ice dynamics against scaling of geometry and physical parameters |
title_fullStr |
Similitude of ice dynamics against scaling of geometry and physical parameters |
title_full_unstemmed |
Similitude of ice dynamics against scaling of geometry and physical parameters |
title_sort |
similitude of ice dynamics against scaling of geometry and physical parameters |
publisher |
Copernicus Publications |
publishDate |
2016 |
url |
https://doi.org/10.5194/tc-10-1753-2016 https://doaj.org/article/e50c97b29c7e492e89eceb71b9013360 |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Vol 10, Iss 4, Pp 1753-1769 (2016) |
op_relation |
http://www.the-cryosphere.net/10/1753/2016/tc-10-1753-2016.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 1994-0416 1994-0424 doi:10.5194/tc-10-1753-2016 https://doaj.org/article/e50c97b29c7e492e89eceb71b9013360 |
op_doi |
https://doi.org/10.5194/tc-10-1753-2016 |
container_title |
The Cryosphere |
container_volume |
10 |
container_issue |
4 |
container_start_page |
1753 |
op_container_end_page |
1769 |
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1766031079359119360 |