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The Flow of Ice Sheets and Ice Shelves

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Continuum Mechanics in Environmental Sciences and Geophysics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 337))

Abstract

A brief survey of the mathematical and numerical modelling of ice sheet and ice shelf flows is presented, emphasising the developments over the last decade. For the very slow gravity driven flow of natural ice masses over time scales of thousands of years, the ice is modelled by an incompressible non-linearly viscous fluid with a temperature dependent rate factor. The conservation laws of mass, linear momentum and energy are formulated, together with the free surface conditions and basal conditions for a grounded sheet and a floating shelf. A systematic reduction of the equations for both sheet and shelf is developed by the introduction of dimensionless variables and stretched co-ordinates, which are motivated by the forms of the sheet profiles sought, and the necessary assumptions are drawn out. Analytic progress is made for restricted flow configurations. The failure of depth-integrated equations to provide a valid approximation in more general configurations is noted. A binary mixture theory is developed for co-existing ice and water in extensive melt zones.

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Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

    L. W. Morland

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  1. Technische Hochschule Darmstadt, Germany

    K. Hutter

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© 1993 Springer-Verlag Wien

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Morland, L.W. (1993). The Flow of Ice Sheets and Ice Shelves. In: Hutter, K. (eds) Continuum Mechanics in Environmental Sciences and Geophysics. International Centre for Mechanical Sciences, vol 337. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2600-4_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2600-4_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82449-8

  • Online ISBN: 978-3-7091-2600-4

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