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.…
Author details: | Johannes FeldmannORCiDGND, Anders LevermannORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-412441 |
DOI: | https://doi.org/10.25932/publishup-41244 |
ISSN: | 1866-8372 |
Title of parent work (English): | Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (564) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/01/31 |
Publication year: | 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 |
Number of pages: | 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 |
DDC classification: | 9 Geschichte und Geografie / 91 Geografie, Reisen / 910 Geografie, Reisen |
Peer review: | Referiert |
Publishing method: | Open Access |
Grantor: | Copernicus |
License (German): | CC-BY - Namensnennung 4.0 International |