Differential Geometry of Ice Flow
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...
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ftdoajarticles:oai:doaj.org/article:6a62511828684a259f1c711829f50049 2023-05-15T13:43:33+02:00 Differential Geometry of Ice Flow Felix S. L. Ng G. Hilmar Gudmundsson Edward C. King 2018-10-01T00:00:00Z https://doi.org/10.3389/feart.2018.00161 https://doaj.org/article/6a62511828684a259f1c711829f50049 EN eng Frontiers Media S.A. https://www.frontiersin.org/article/10.3389/feart.2018.00161/full https://doaj.org/toc/2296-6463 2296-6463 doi:10.3389/feart.2018.00161 https://doaj.org/article/6a62511828684a259f1c711829f50049 Frontiers in Earth Science, Vol 6 (2018) ice sheets ice streams flow direction convergence curvature symmetry breaking Science Q article 2018 ftdoajarticles https://doi.org/10.3389/feart.2018.00161 2022-12-31T04:25:48Z 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. Article in Journal/Newspaper Antarc* Antarctic Ice Sheet Directory of Open Access Journals: DOAJ Articles Antarctic Curl ENVELOPE(-63.071,-63.071,-70.797,-70.797) The Antarctic Frontiers in Earth Science 6 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
ice sheets ice streams flow direction convergence curvature symmetry breaking Science Q |
spellingShingle |
ice sheets ice streams flow direction convergence curvature symmetry breaking Science Q Felix S. L. Ng G. Hilmar Gudmundsson Edward C. King Differential Geometry of Ice Flow |
topic_facet |
ice sheets ice streams flow direction convergence curvature symmetry breaking Science Q |
description |
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. |
format |
Article in Journal/Newspaper |
author |
Felix S. L. Ng G. Hilmar Gudmundsson Edward C. King |
author_facet |
Felix S. L. Ng G. Hilmar Gudmundsson Edward C. King |
author_sort |
Felix S. L. Ng |
title |
Differential Geometry of Ice Flow |
title_short |
Differential Geometry of Ice Flow |
title_full |
Differential Geometry of Ice Flow |
title_fullStr |
Differential Geometry of Ice Flow |
title_full_unstemmed |
Differential Geometry of Ice Flow |
title_sort |
differential geometry of ice flow |
publisher |
Frontiers Media S.A. |
publishDate |
2018 |
url |
https://doi.org/10.3389/feart.2018.00161 https://doaj.org/article/6a62511828684a259f1c711829f50049 |
long_lat |
ENVELOPE(-63.071,-63.071,-70.797,-70.797) |
geographic |
Antarctic Curl The Antarctic |
geographic_facet |
Antarctic Curl The Antarctic |
genre |
Antarc* Antarctic Ice Sheet |
genre_facet |
Antarc* Antarctic Ice Sheet |
op_source |
Frontiers in Earth Science, Vol 6 (2018) |
op_relation |
https://www.frontiersin.org/article/10.3389/feart.2018.00161/full https://doaj.org/toc/2296-6463 2296-6463 doi:10.3389/feart.2018.00161 https://doaj.org/article/6a62511828684a259f1c711829f50049 |
op_doi |
https://doi.org/10.3389/feart.2018.00161 |
container_title |
Frontiers in Earth Science |
container_volume |
6 |
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1766190519611817984 |