Creep Instability of Ice Sheets
Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heatin...
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Cambridge University Press (CUP)
1976
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Online Access: | http://dx.doi.org/10.1017/s0022143000031622 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031622 |
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crcambridgeupr:10.1017/s0022143000031622 2024-03-03T08:46:08+00:00 Creep Instability of Ice Sheets Clarke, Garry K.C. 1976 http://dx.doi.org/10.1017/s0022143000031622 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031622 en eng Cambridge University Press (CUP) Journal of Glaciology volume 16, issue 74, page 278-279 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1976 crcambridgeupr https://doi.org/10.1017/s0022143000031622 2024-02-08T08:40:37Z Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λ m of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions. In this special case the stability condition is if the bed is frozen and if it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π( a/K )1/2 if the bed is frozen or h = π ( a/K )1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λ m ) –1 is the time constant for the mth eigenfunction. Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and T B at the bed is considerably more stable than a slab held at constant stressσ B and a constant temperature T B . Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, ... Article in Journal/Newspaper Journal of Glaciology Cambridge University Press Journal of Glaciology 16 74 278 279 |
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Open Polar |
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Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes Clarke, Garry K.C. Creep Instability of Ice Sheets |
topic_facet |
Earth-Surface Processes |
description |
Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λ m of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions. In this special case the stability condition is if the bed is frozen and if it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π( a/K )1/2 if the bed is frozen or h = π ( a/K )1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λ m ) –1 is the time constant for the mth eigenfunction. Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and T B at the bed is considerably more stable than a slab held at constant stressσ B and a constant temperature T B . Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, ... |
format |
Article in Journal/Newspaper |
author |
Clarke, Garry K.C. |
author_facet |
Clarke, Garry K.C. |
author_sort |
Clarke, Garry K.C. |
title |
Creep Instability of Ice Sheets |
title_short |
Creep Instability of Ice Sheets |
title_full |
Creep Instability of Ice Sheets |
title_fullStr |
Creep Instability of Ice Sheets |
title_full_unstemmed |
Creep Instability of Ice Sheets |
title_sort |
creep instability of ice sheets |
publisher |
Cambridge University Press (CUP) |
publishDate |
1976 |
url |
http://dx.doi.org/10.1017/s0022143000031622 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031622 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 16, issue 74, page 278-279 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000031622 |
container_title |
Journal of Glaciology |
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16 |
container_issue |
74 |
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278 |
op_container_end_page |
279 |
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1792502078590943232 |