Ng, F.S. orcid.org/0000-0001-6352-0351, Gudmundsson, G.H. and King, E.C. (2018) Differential geometry of ice flow. Frontiers in Earth Science, 6. 161. ISSN 2296-6463
Abstract
Flowlines on ice sheets and glaciers form complex patterns. To explore their role in ice routing and extend the language for studying such patterns, we develop a theory of flow convergence and curvature in plan view. These geometric quantities respectively equal the negative divergence of the vector field of ice-flow direction and the curl of this field. From the first of these two fundamental results, we show that flow in individual catchments of an ice sheet can converge (despite its overall spreading) because ice divides are loci of strong divergence, and that a sign bifurcation in convergence occurs during ice-sheet 'symmetry breaking' (the transition from near-radial spreading to spreading with substantial azimuthal velocities) and during the formation of ice-stream tributary networks. We also uncover the topological control behind balance-flux distributions across ice masses. Notably, convergence participates in mass conservation along flowlines to amplify ice flux via a positive feedback; thus the convergence field governs the form of ice-stream networks simulated by balance-velocity models. The theory provides a roadmap for understanding the tower-shaped plot of flow speed versus convergence for the Antarctic Ice Sheet.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Ng, Gudmundsson and King. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
Keywords: | Ice sheets; Ice streams; flow direction; convergence; curvature; symmetry breaking; Balance velocity; Antarctica |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Geography (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 01 Oct 2018 09:38 |
Last Modified: | 24 Oct 2018 08:53 |
Published Version: | https://doi.org/10.3389/feart.2018.00161 |
Status: | Published |
Publisher: | Frontiers Media |
Refereed: | Yes |
Identification Number: | 10.3389/feart.2018.00161 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:136294 |