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Influence of non-uniform temperature distribution on the steady motion of ice sheets

Published online by Cambridge University Press:  20 April 2006

L. W. Morland  and
G. D. Smith
L. W. Morland
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NR4 7TJ, U.K.
G. D. Smith
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NR4 7TJ, U.K.
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Abstract

The plane steady flow of a grounded ice sheet is analysed under the assumption that the ice behaves as a nonlinearly viscous fluid with a strongly temperature-dependent rate factor. It is supposed that the accumulation/ablation distribution on the (unknown) free surface is prescribed, and that there is a given basal sliding condition connecting the tangential velocity, tangential traction and normal pressure. The basal boundary is defined as the smooth contour which describes the mean topography viewed on the ice-sheet lengthscale, and is assumed to have small slope. The perturbation analysis which reduces the isothermal or constant rate factor equations to an ordinary differential equation for the leading-order profile is now extended with similar success to the non-isothermal problem when the temperature distribution is prescribed. That is, the thermomechanically coupled energy balance is not solved, but families of temperature distributions qualitatively compatible with observed patterns are adopted to exhibit the effects of significant creep-rate variation with temperature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 113 - 133
Copyright
© 1984 Cambridge University Press

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References

Boulton, G. S., Smith, G. D. & Morland, L. W. 1983 The reconstruction of former ice sheets and their mass balance characteristics using a nonlinearly viscous flow model. J. Glaciol. (in the press).Google Scholar
Glen, J. W. 1955 The creep of polycrystalline ice. Proc. R. Soc. Lond. A 228, 515–538.Google Scholar
Johnson, R. E. & McMeeking, R. M. 1982 Near-surface flow in glaciers obeying Glen's Law. Univ. Illinois T & AM Rep. 454.Google Scholar
Jones, A. S. 1978 The dependence of temperature profiles in ice sheets on longitudinal variations in velocity and surface temperature. J. Glaciol. 20, 31–39.Google Scholar
Hutter, K. 1982 Dynamics of glaciers and large ice masses. Ann. Rev. Fluid Mech. 14, 87–130.Google Scholar
Hutter, K. 1983 Theoretical Glaciology, Reidel.
Mellor, M. & Testa, R. 1969 Effect of temperature on the creep of ice. J. Glaciol. 8, 131–145.Google Scholar
Morland, L. W. 1983 Thermomechanical balances of ice sheet flows. Submitted to Geophys. Astrophys. Fluid Dyn.Google Scholar
Morland, L. W. & Johnson, I. R. 1980 Steady motion of ice sheets. J. Glaciol. 25, 229–246.Google Scholar
Morland, L. W. & Johnson, I. R. 1982 Effects of bed inclination and topography on steady isothermal ice sheets. J. Glaciol. 28, 71–90.Google Scholar
Morland, L. W. & Shoemaker, E. M. 1982 Ice shelf balances. Cold Regions Sci. Tech. 5, 235–251.Google Scholar
Morland, L. W., Smith, G. D. & Boulton, G. S. 1983 Basal sliding relations deduced from ice sheet data. J. Glaciol. (in the press).Google Scholar
Nye, J. F. 1959 The motion of ice sheets and glaciers. J. Glaciol. 3, 493–507.Google Scholar
Smith, G. D. & Morland, L. W. 1981 Viscous relations for the steady creep of polycrystalline ice. Cold Regions Sci. Tech. 5, 141–150.Google Scholar