Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology
Abstract The problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude o...
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Cambridge University Press (CUP)
1987
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Online Access: | http://dx.doi.org/10.1017/s0022143000008674 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000008674 |
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crcambridgeupr:10.1017/s0022143000008674 2024-03-03T08:45:28+00:00 Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology Reeh, Niels 1987 http://dx.doi.org/10.1017/s0022143000008674 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000008674 en eng Cambridge University Press (CUP) Journal of Glaciology volume 33, issue 114, page 177-185 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1987 crcambridgeupr https://doi.org/10.1017/s0022143000008674 2024-02-08T08:40:23Z Abstract The problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude of the basal undulations to the ice thickness as perturbation parameter, equations to the first order for the velocity and pressure perturbations are set up and solved. The study shows that when the widths of the basal undulations are larger than 2–3 times their lengths, the finite width of the undulations has only a minor influence on the flow, which to a good approximation may be considered two-dimensional. However, as the ratio between the longitudinal and the transverse wavelength L/W increases, the three-dimensional flow effects becomes substantial. If, for example, the ratio of L to W exceeds 3, surface amplitudes are reduced by more than one order of magnitude as compared to the two-dimensional case. The L/W ratio also influences the depth variation of the amplitudes of internal layers and the depth variation of perturbation velocities and strain-rates. With increasing L/W ratio, the changes of these quantities are concentrated in a near-bottom layer of decreasing thickness. Furthermore, it is shown, that the azimuth of the velocity vector may change by up to 10° between the surface and the base of the ice sheet, and that significant transverse flow may occur at depth without manifesting itself at the surface to any significant degree. Article in Journal/Newspaper Ice Sheet Journal of Glaciology Cambridge University Press Journal of Glaciology 33 114 177 185 |
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Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes Reeh, Niels Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
topic_facet |
Earth-Surface Processes |
description |
Abstract The problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude of the basal undulations to the ice thickness as perturbation parameter, equations to the first order for the velocity and pressure perturbations are set up and solved. The study shows that when the widths of the basal undulations are larger than 2–3 times their lengths, the finite width of the undulations has only a minor influence on the flow, which to a good approximation may be considered two-dimensional. However, as the ratio between the longitudinal and the transverse wavelength L/W increases, the three-dimensional flow effects becomes substantial. If, for example, the ratio of L to W exceeds 3, surface amplitudes are reduced by more than one order of magnitude as compared to the two-dimensional case. The L/W ratio also influences the depth variation of the amplitudes of internal layers and the depth variation of perturbation velocities and strain-rates. With increasing L/W ratio, the changes of these quantities are concentrated in a near-bottom layer of decreasing thickness. Furthermore, it is shown, that the azimuth of the velocity vector may change by up to 10° between the surface and the base of the ice sheet, and that significant transverse flow may occur at depth without manifesting itself at the surface to any significant degree. |
format |
Article in Journal/Newspaper |
author |
Reeh, Niels |
author_facet |
Reeh, Niels |
author_sort |
Reeh, Niels |
title |
Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
title_short |
Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
title_full |
Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
title_fullStr |
Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
title_full_unstemmed |
Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology |
title_sort |
steady-state three-dimensional ice flow over an undulating base: first-order theory with linear ice rheology |
publisher |
Cambridge University Press (CUP) |
publishDate |
1987 |
url |
http://dx.doi.org/10.1017/s0022143000008674 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000008674 |
genre |
Ice Sheet Journal of Glaciology |
genre_facet |
Ice Sheet Journal of Glaciology |
op_source |
Journal of Glaciology volume 33, issue 114, page 177-185 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000008674 |
container_title |
Journal of Glaciology |
container_volume |
33 |
container_issue |
114 |
container_start_page |
177 |
op_container_end_page |
185 |
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1792501022664425472 |