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...
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fttriple:oai:gotriple.eu:oai:doaj.org/article:01cf71a23b514ae58a51217c69e637c3 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 G. H. Gudmundsson 2008-07-01 http://www.the-cryosphere.net/2/77/2008/tc-2-77-2008.pdf https://doaj.org/article/01cf71a23b514ae58a51217c69e637c3 en eng Copernicus Publications 1994-0416 1994-0424 http://www.the-cryosphere.net/2/77/2008/tc-2-77-2008.pdf https://doaj.org/article/01cf71a23b514ae58a51217c69e637c3 undefined The Cryosphere, Vol 2, Iss 2, Pp 77-93 (2008) geo envir Journal Article https://vocabularies.coar-repositories.org/resource_types/c_6501/ 2008 fttriple 2023-01-22T17:53:07Z 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 Unknown Weertman ENVELOPE(-67.753,-67.753,-66.972,-66.972) |
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geo envir G. H. Gudmundsson Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
topic_facet |
geo envir |
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 |
G. H. Gudmundsson |
author_facet |
G. H. Gudmundsson |
author_sort |
G. H. Gudmundsson |
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 |
http://www.the-cryosphere.net/2/77/2008/tc-2-77-2008.pdf https://doaj.org/article/01cf71a23b514ae58a51217c69e637c3 |
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_source |
The Cryosphere, Vol 2, Iss 2, Pp 77-93 (2008) |
op_relation |
1994-0416 1994-0424 http://www.the-cryosphere.net/2/77/2008/tc-2-77-2008.pdf https://doaj.org/article/01cf71a23b514ae58a51217c69e637c3 |
op_rights |
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1766030264669044736 |