Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations
Abstract The basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, u...
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Cambridge University Press (CUP)
1997
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Online Access: | http://dx.doi.org/10.1017/s0022143000002823 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000002823 |
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crcambridgeupr:10.1017/s0022143000002823 2024-03-03T08:45:58+00:00 Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations Gudmundsson, G. Hilmar 1997 http://dx.doi.org/10.1017/s0022143000002823 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000002823 en eng Cambridge University Press (CUP) Journal of Glaciology volume 43, issue 143, page 71-79 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1997 crcambridgeupr https://doi.org/10.1017/s0022143000002823 2024-02-08T08:41:37Z Abstract The basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : = ak < 0.138, where a is the amplitude and k is the wave number. As ε increases from zerо to this critical value, the vertical position of the velocity maximum moves from kz = 1 to kz ≈ 1.98, where z is the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts from kz = 1 towards the bed line as ε increases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock. Article in Journal/Newspaper Journal of Glaciology Cambridge University Press Journal of Glaciology 43 143 71 79 |
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Open Polar |
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Cambridge University Press |
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crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
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Earth-Surface Processes Gudmundsson, G. Hilmar Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
topic_facet |
Earth-Surface Processes |
description |
Abstract The basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : = ak < 0.138, where a is the amplitude and k is the wave number. As ε increases from zerо to this critical value, the vertical position of the velocity maximum moves from kz = 1 to kz ≈ 1.98, where z is the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts from kz = 1 towards the bed line as ε increases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock. |
format |
Article in Journal/Newspaper |
author |
Gudmundsson, G. Hilmar |
author_facet |
Gudmundsson, G. Hilmar |
author_sort |
Gudmundsson, G. Hilmar |
title |
Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
title_short |
Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
title_full |
Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
title_fullStr |
Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
title_full_unstemmed |
Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
title_sort |
basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations |
publisher |
Cambridge University Press (CUP) |
publishDate |
1997 |
url |
http://dx.doi.org/10.1017/s0022143000002823 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000002823 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 43, issue 143, page 71-79 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000002823 |
container_title |
Journal of Glaciology |
container_volume |
43 |
container_issue |
143 |
container_start_page |
71 |
op_container_end_page |
79 |
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1792501696979533824 |