Mathematical Model of a Three-Dimensional Non-Isothermal Glacier
Abstract In the case of a non-isothermal glacier it is necessary to integrate the equations of dynamics together with the equation of heat conduction, heat transfer, and heat generation because of the interdependence (1) of strain-rate of ice on its temperature, and (2) of ice temperature on the rat...
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Cambridge University Press (CUP)
1976
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crcambridgeupr:10.1017/s0022143000031737 2024-03-03T08:46:04+00:00 Mathematical Model of a Three-Dimensional Non-Isothermal Glacier Grigoryan, S.S. Krass, M.S. Shumskiy, P.A. 1976 http://dx.doi.org/10.1017/s0022143000031737 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031737 en eng Cambridge University Press (CUP) Journal of Glaciology volume 16, issue 74, page 308-309 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1976 crcambridgeupr https://doi.org/10.1017/s0022143000031737 2024-02-08T08:40:23Z Abstract In the case of a non-isothermal glacier it is necessary to integrate the equations of dynamics together with the equation of heat conduction, heat transfer, and heat generation because of the interdependence (1) of strain-rate of ice on its temperature, and (2) of ice temperature on the rate of heat transfer by moving ice and on the intensity of heat generation in its strain. In view of the complexity of the whole system of equations, simplified mathematical models have been constructed for dynamically different glaciers. The present model concerns land glaciers with thicknesses much less than their horizontal dimensions and radii of curvature of large bottom irregularities, so that the method of a thin boundary layer may be used. The principal assumption is the validity of averaging over a distance of the order of magnitude of ice thickness. Two component shear stresses parallel to the bottom in glaciers of this type considerably exceed the normal stresses and the third shear stress, so the dynamics are described by a statically determined system of equations. For the general case, expressions for the stresses have been obtained in dimensionless affine orthogonal curvilinear coordinates, parallel and normal to the glacier bottom, and taking into account the geometry of the lower and upper surfaces. The statically undetermined problem for ice divides is solved using the equations of continuity and rheology, so the result for stresses depends considerably on temperature distribution. In the case of a flat bottom the dynamics of an ice divide is determined by the curvature of the upper surface. The calculation of the interrelating velocity and temperature distributions is made by means of the iteration of solutions (1) for the components of velocity from the stress expressions using the rheological equations (a power law or the more precise hyberbolic one) with the assigned temperature distribution, and (2) for the temperature with the assigned velocity distribution. The temperature distribution in the ... Article in Journal/Newspaper Journal of Glaciology Cambridge University Press Journal of Glaciology 16 74 308 309 |
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Open Polar |
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Cambridge University Press |
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language |
English |
topic |
Earth-Surface Processes |
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Earth-Surface Processes Grigoryan, S.S. Krass, M.S. Shumskiy, P.A. Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
topic_facet |
Earth-Surface Processes |
description |
Abstract In the case of a non-isothermal glacier it is necessary to integrate the equations of dynamics together with the equation of heat conduction, heat transfer, and heat generation because of the interdependence (1) of strain-rate of ice on its temperature, and (2) of ice temperature on the rate of heat transfer by moving ice and on the intensity of heat generation in its strain. In view of the complexity of the whole system of equations, simplified mathematical models have been constructed for dynamically different glaciers. The present model concerns land glaciers with thicknesses much less than their horizontal dimensions and radii of curvature of large bottom irregularities, so that the method of a thin boundary layer may be used. The principal assumption is the validity of averaging over a distance of the order of magnitude of ice thickness. Two component shear stresses parallel to the bottom in glaciers of this type considerably exceed the normal stresses and the third shear stress, so the dynamics are described by a statically determined system of equations. For the general case, expressions for the stresses have been obtained in dimensionless affine orthogonal curvilinear coordinates, parallel and normal to the glacier bottom, and taking into account the geometry of the lower and upper surfaces. The statically undetermined problem for ice divides is solved using the equations of continuity and rheology, so the result for stresses depends considerably on temperature distribution. In the case of a flat bottom the dynamics of an ice divide is determined by the curvature of the upper surface. The calculation of the interrelating velocity and temperature distributions is made by means of the iteration of solutions (1) for the components of velocity from the stress expressions using the rheological equations (a power law or the more precise hyberbolic one) with the assigned temperature distribution, and (2) for the temperature with the assigned velocity distribution. The temperature distribution in the ... |
format |
Article in Journal/Newspaper |
author |
Grigoryan, S.S. Krass, M.S. Shumskiy, P.A. |
author_facet |
Grigoryan, S.S. Krass, M.S. Shumskiy, P.A. |
author_sort |
Grigoryan, S.S. |
title |
Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
title_short |
Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
title_full |
Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
title_fullStr |
Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
title_full_unstemmed |
Mathematical Model of a Three-Dimensional Non-Isothermal Glacier |
title_sort |
mathematical model of a three-dimensional non-isothermal glacier |
publisher |
Cambridge University Press (CUP) |
publishDate |
1976 |
url |
http://dx.doi.org/10.1017/s0022143000031737 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000031737 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 16, issue 74, page 308-309 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000031737 |
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Journal of Glaciology |
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16 |
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74 |
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308 |
op_container_end_page |
309 |
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1792501925592170496 |