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A three-dimensional ice-sheet flow solution

  • L.W. Morland (a1)

Abstract

An accurate three-dimensional reduced model (shallow-ice approximation) flow with velocity depending on all three spatial coordinates is constructed for the commonly adopted isotropic viscous law with temperature-dependent rate factor. The solution is for steady flow with a prescribed temperature distribution, but can be extended to flow with a coupled energy balance, and to unsteady flow. The accuracy hinges on the reduction to a two-point ordinary differential equation problem for the surface profile, on an unknown span, for which established accurate numerical methods are available. This is achieved by setting one horizontal velocity component in elliptic cylindrical coordinates to zero, but the other two components depend on all three spatial variables. While not of direct physical interest, such an ‘exact’ solution is valuable as a test solution for the large-scale numerical codes commonly used in ice-sheet modelling, which have not yet been subjected to such a comparison.

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Copyright

References

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Brandt, L. 1947. Vector and tensor analysis. London, Wiley.
Bueler, E., Brown, J. and Lingle, C.. 2007. Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification. J. Glaciol., 53(182), 499516.
Cliffe, K.A. and Morland, L.W.. 2000. Full and reduced model solutions of steady axi-symmetric ice sheet flow over small and large bed topography slopes. Contin. Mech. Thermodyn., 12(3), 195216.
Cliffe, K.A. and Morland, L.W.. 2001. A thermo-mechanically coupled test case for axi-symmetric ice sheet flow. Contin. Mech.Thermodyn., 13(2), 135148.
Cliffe, K.A. and Morland, L.W.. 2002. Full and reduced model solutions of steady axi-symmetric ice sheet flow over bed topography with moderate slope. Contin. Mech. Thermodyn., 14(2), 149164.
Cliffe, K.A. and Morland, L.W.. 2004. Full and reduced model solutions of unsteady axi-symmetric ice sheet flow over a flat bed. Contin. Mech. Thermodyn., 16(5), 481494.
Glen, J.W. 1955. The creep of polycrystalline ice. Proc. R. Soc. London, Ser. A, 228(1175), 519538.
Hindmarsh, R.C.A. 2001. Notes on basic glaciological computational methods and algorithms. In Straughan, B., Greve, R., Ehrentraut, H. and Wang, Y., eds. Continuum mechanics and applications in geophysics and the environment. Berlin, etc., Springer-Verlag, 222249.
Hindmarsh, R.C.A. 2004. A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling. J. Geophys. Res., 109(F1), F01012. (10.1029/2003JF000065.)
Magnus, W., Oberhettinger, F. and Soni, R.P. 1966. Formulas and theorems for the special functions of mathematical physics. Third edition. Berlin, etc., Springer-Verlag.
Mellor, M. and Testa, R.. 1969. Effect of temperature on the creep of ice. J. Glaciol., 8(52), 131145.
Morland, L.W. 1984. Thermomechanical balances of ice sheet flows. Geophys. Astrophys. Fluid Dyn., 29(1–4), 237266.
Morland, L.W. 1997. Radially symmetric ice sheet flow. Philos. Trans. R. Soc. London, Ser. A, 355(1730), 18731904.
Morland, L.W. 2000. Steady plane isothermal linearly viscous flow of ice sheets on beds with moderate slope topography. Proc. R. Soc. London, Ser. A, 456(1999), 17111739
Morland, L.W. 2001. Influence of bed topography on steady plane ice sheet flow. In Straughan, B., Greve, R., Ehrentraut, H. and Wang, Y., eds. Continuum mechanics and applications in geophysics and the environment. Berlin, etc., Springer-Verlag, 276304.
Morland, L.W. and Johnson, I.R.. 1980. Steady motion of ice sheets. J. Glaciol., 25(92), 229246.
Payne, A.J. and Baldwin, D.J.. 2000. Analysis of ice-flow instabilities identified in the EISMINT intercomparison exercise. Ann. Glaciol., 30, 204210.
Payne, A.J. and 10 others. 2000. Results from the EISMINT model intercomparison: the effects of thermomechanical coupling. J. Glaciol., 46(153), 227238.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. 1992. Numerical recipes in FORTRAN: the art of scientific computing. Second edition. Cambridge, Cambridge University Press.
Simmonds, J.G. 1997. A brief on tensor analysis. Second edition. New York, Springer-Verlag.
Smith, G.D. and Morland, L.W.. 1981. Viscous relations for the steady creep of polycrystalline ice. Cold Reg. Sci. Technol., 5(2), 141150.

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