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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 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 investigateThe 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.show moreshow less

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Metadaten
Author:Johannes FeldmannORCiDGND, Anders LevermannORCiDGND
URN:urn:nbn:de:kobv:517-opus4-412441
DOI:https://doi.org/10.25932/publishup-41244
ISSN:1866-8372
Parent Title (English):Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (564)
Document Type:Postprint
Language:English
Date of first Publication:2019/01/31
Year of Completion:2016
Publishing Institution:Universität Potsdam
Release Date:2019/01/31
Tag:Pine Island; West Antarctica; collapse; flow; full-stokes model; grounding line motion; sensitivity; sheet models; shelf; stream-B
Issue:564
Pagenumber:17
First Page:1753
Last Page:1769
Source:The Cryosphere 10 (2016) 4, pp. 1753–1969 DOI 10.5194/tc-10-1753–2016
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:9 Geschichte und Geografie / 91 Geografie, Reisen / 910 Geografie, Reisen
Peer Review:Referiert
Publication Way:Open Access
Grantor:Copernicus
Licence (German):License LogoCreative Commons - Namensnennung, 4.0 International