Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients
Abstract A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the f...
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Cambridge University Press (CUP)
1995
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Online Access: | http://dx.doi.org/10.1017/s002214300001621x https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002214300001621X |
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crcambridgeupr:10.1017/s002214300001621x 2024-10-13T14:08:40+00:00 Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients Blatter, Heinz 1995 http://dx.doi.org/10.1017/s002214300001621x https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002214300001621X en eng Cambridge University Press (CUP) Journal of Glaciology volume 41, issue 138, page 333-344 ISSN 0022-1430 1727-5652 journal-article 1995 crcambridgeupr https://doi.org/10.1017/s002214300001621x 2024-09-18T04:03:52Z Abstract A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unity and approximating the derivatives in the horizontal direction by centered finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly. The algorithm can be used for a wide rangŠµ of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation. Article in Journal/Newspaper Journal of Glaciology Cambridge University Press Journal of Glaciology 41 138 333 344 |
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Open Polar |
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Cambridge University Press |
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crcambridgeupr |
language |
English |
description |
Abstract A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unity and approximating the derivatives in the horizontal direction by centered finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly. The algorithm can be used for a wide rangŠµ of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation. |
format |
Article in Journal/Newspaper |
author |
Blatter, Heinz |
spellingShingle |
Blatter, Heinz Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
author_facet |
Blatter, Heinz |
author_sort |
Blatter, Heinz |
title |
Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
title_short |
Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
title_full |
Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
title_fullStr |
Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
title_full_unstemmed |
Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
title_sort |
velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients |
publisher |
Cambridge University Press (CUP) |
publishDate |
1995 |
url |
http://dx.doi.org/10.1017/s002214300001621x https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002214300001621X |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 41, issue 138, page 333-344 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s002214300001621x |
container_title |
Journal of Glaciology |
container_volume |
41 |
container_issue |
138 |
container_start_page |
333 |
op_container_end_page |
344 |
_version_ |
1812815384828444672 |