Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation
New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding...
Published in: | The Cryosphere |
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Copernicus Publications
2008
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ftnonlinearchiv:oai:noa.gwlb.de:cop_mods_00031288 2023-05-15T16:39:55+02:00 Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation Gudmundsson, G. H. 2008-07 electronic https://doi.org/10.5194/tc-2-77-2008 https://noa.gwlb.de/receive/cop_mods_00031288 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00031242/tc-2-77-2008.pdf https://tc.copernicus.org/articles/2/77/2008/tc-2-77-2008.pdf eng eng Copernicus Publications The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-2-77-2008 https://noa.gwlb.de/receive/cop_mods_00031288 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00031242/tc-2-77-2008.pdf https://tc.copernicus.org/articles/2/77/2008/tc-2-77-2008.pdf uneingeschränkt info:eu-repo/semantics/openAccess article Verlagsveröffentlichung article Text doc-type:article 2008 ftnonlinearchiv https://doi.org/10.5194/tc-2-77-2008 2022-02-08T22:46:49Z New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses. Article in Journal/Newspaper Ice Sheet The Cryosphere Niedersächsisches Online-Archiv NOA Weertman ENVELOPE(-67.753,-67.753,-66.972,-66.972) The Cryosphere 2 2 77 93 |
institution |
Open Polar |
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Niedersächsisches Online-Archiv NOA |
op_collection_id |
ftnonlinearchiv |
language |
English |
topic |
article Verlagsveröffentlichung |
spellingShingle |
article Verlagsveröffentlichung Gudmundsson, G. H. Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
topic_facet |
article Verlagsveröffentlichung |
description |
New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses. |
format |
Article in Journal/Newspaper |
author |
Gudmundsson, G. H. |
author_facet |
Gudmundsson, G. H. |
author_sort |
Gudmundsson, G. H. |
title |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_short |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_full |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_fullStr |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_full_unstemmed |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_sort |
analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
publisher |
Copernicus Publications |
publishDate |
2008 |
url |
https://doi.org/10.5194/tc-2-77-2008 https://noa.gwlb.de/receive/cop_mods_00031288 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00031242/tc-2-77-2008.pdf https://tc.copernicus.org/articles/2/77/2008/tc-2-77-2008.pdf |
long_lat |
ENVELOPE(-67.753,-67.753,-66.972,-66.972) |
geographic |
Weertman |
geographic_facet |
Weertman |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_relation |
The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-2-77-2008 https://noa.gwlb.de/receive/cop_mods_00031288 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00031242/tc-2-77-2008.pdf https://tc.copernicus.org/articles/2/77/2008/tc-2-77-2008.pdf |
op_rights |
uneingeschränkt info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.5194/tc-2-77-2008 |
container_title |
The Cryosphere |
container_volume |
2 |
container_issue |
2 |
container_start_page |
77 |
op_container_end_page |
93 |
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1766030258457280512 |