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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ftleibnizopen:oai:oai.leibnizopen.de:nP0pF4cBdbrxVwz6Qk21 2023-05-15T16:40:27+02:00 Similitude of ice dynamics against scaling of geometry and physical parameters Feldmann, Johannes Levermann, Anders 2016 application/pdf https://doi.org/10.34657/1256 https://oa.tib.eu/renate/handle/123456789/671 eng eng München : European Geopyhsical Union CC BY 3.0 Unported https://creativecommons.org/licenses/by/3.0/ The Cryosphere, Volume 10, Issue 4, Page 1753-1769 cryosphere dimension less number fluid dynamics geometryice flow ice mechanics ice sheet isotherm mass balance numerical model physical property stress field 550 article Text 2016 ftleibnizopen https://doi.org/10.34657/1256 2023-03-26T23:31:20Z 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. publishedVersion Article in Journal/Newspaper Ice Sheet The Cryosphere LeibnizOpen (The Leibniz Association) |
institution |
Open Polar |
collection |
LeibnizOpen (The Leibniz Association) |
op_collection_id |
ftleibnizopen |
language |
English |
topic |
cryosphere dimension less number fluid dynamics geometryice flow ice mechanics ice sheet isotherm mass balance numerical model physical property stress field 550 |
spellingShingle |
cryosphere dimension less number fluid dynamics geometryice flow ice mechanics ice sheet isotherm mass balance numerical model physical property stress field 550 Feldmann, Johannes Levermann, Anders Similitude of ice dynamics against scaling of geometry and physical parameters |
topic_facet |
cryosphere dimension less number fluid dynamics geometryice flow ice mechanics ice sheet isotherm mass balance numerical model physical property stress field 550 |
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. publishedVersion |
format |
Article in Journal/Newspaper |
author |
Feldmann, Johannes Levermann, Anders |
author_facet |
Feldmann, Johannes Levermann, Anders |
author_sort |
Feldmann, Johannes |
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 |
München : European Geopyhsical Union |
publishDate |
2016 |
url |
https://doi.org/10.34657/1256 https://oa.tib.eu/renate/handle/123456789/671 |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Volume 10, Issue 4, Page 1753-1769 |
op_rights |
CC BY 3.0 Unported https://creativecommons.org/licenses/by/3.0/ |
op_doi |
https://doi.org/10.34657/1256 |
_version_ |
1766030846466195456 |