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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Published in:Journal of Glaciology
Main Author: Reeh, Niels
Format: Article in Journal/Newspaper
Language:English
Published: Cambridge University Press (CUP) 1987
Subjects:
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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spelling 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
institution 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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