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Plane ice-sheet flow with evolving orthotopic fabric

  • R. Staroszczyk (a1) and L.W. Morland (a1)


A plane, gravity-driven, steady flow of an isothermal ice sheet over a horizontal bedrock, with no-slip basal conditions, is considered. The ice is modelled as a linearly viscous, incompressible and anisotropic fluid, with evolving orthotropic fabric that depends on local strain rates and deformations. For a fixed, free-surface elevation, the ice-accumulation rates necessary to maintain the prescribed geometry are calculated by using the finite-element method, together with the velocities and stresses. Numerical simulations have been carried out for different combinations of enhancement factors for compression and shear in order to investigate their effect on the rate of flow. The results obtained have shown that, apart from the near-divide region, the global flow rate is nearly proportional to the magnitude of the shear-enhancement factor and is very little sensitive to the value of the compression enhancement factor. Normalized velocity-depth profiles have been compared for the anisotropic and isotropic ice and it has been found that significant differences occur only in a region near the ice divide. Direct shear stresses are little affected by the ice anisotropy, but the longitudinal deviatoric stresses in a part of the ice sheet are significantly increased compared to the isotropic ice flow.

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Boehler, J. P., ed. 1987. Application of tensor function, in solid mechanics. Berlin, etc., Springer-Verlag. (International Centre for the Mechanical Sciences, Course 292.)
Budd, W. F. and Jacka, T. H.. 1989. A review of ice rheology for ice sheet modelling. Cold Reg. Set. Technol, 16(2), 107144.
Chorin, A.J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comput. Phys., 2,1226.
Dahl-Jensen, D. 1989. Steady thermomechanical flow along two-dimensional flow lines in large grounded ice sheets. J. Geophys. Res., 94 (B8), 10,35510,362
Fabre, A., Letréguilly, A., Ritz, C. and Mangeney, A. 1995. Greenland under changing climates: sensitivity experiments with a new three-dimensional ice-sheet model. Ann. Glaciol, 21,17.
Fowler, A. C. and Larson, D. A.. 1978. On the flow of polythermal glaciers. I: Model and preliminary analysis. Proc. R. Soc. London, Ser. A, 363(1713), 217242.
Gagliardini, O. and Meyssonnier, J.. 1999. Analytical derivations for the behaviour and fabric evolution of a linear orthotropic ice polycrystal. J. Geophys. Res., 104(B8), 17,79717,809.
Hanson, B 1995. A fully three-dimensional finite-element model applied to velocities on Storglaciaren, Sweden. J. Glacial. , 41 (137), 91102.
Herterich, K. 1988. A three-dimensional model of the Antarctic ice sheet. Ann. Glacial, 11, 3235.
Hindmarsh, R. C. A., Morland, L.W., Boulton, G. S. and Hutter, K.. 1987. The unsteady plane flow of ice-sheets: a parabolic problem with two moving boundaries. Geophys. Astrophys. Fluid Dyn., 39(3), 183225.
Hirsch, C. 1992. .Numerical computation of internal and external flows. Vol. 2. Chichester, Wiley.
Hodge, S. M. 1985. Two-dimensional, time-dependent modeling of an arbitrarily shaped ice mass with the finite-element technique. J. Glacial., 31 (109), 350359.
Hooke, R. Left, Raymond, C. F, Hotchkiss, R. L. and Gustafson, R. J.. 1979. Calculations of velocity and temperature in a polar glacier using the finite-element method. J. Glacial, 24(90), 131146.
Hutter, K. 1981. The effect of longitudinal strain on the shear stress of an ice sheet: in defence of using stretched coordinates. J. Glacial, 27(95), 3956.
Hutter, K. 1983. Theoretical glaciology; material science of ice and the mechanics of glaciers and ice sheets. Dordrecht, etc., D. Reidel Publishing Co.; Tokyo, Terra Scientific Publishing Co.
Hutter, K., Yakowitz, S. and Szidarovszky, F 1986. A numerical study of plane ice-sheet flow. J. Glacial, 32(111), 139160.
Huybrechts, P. 1990. A 3–D model for the Antarctic ice sheet: a sensitivity study on the glacial-interglacial contrast. Climate Dyn., 5(2), 7992.
Hvidberg, C. S. 1996. Steady-state thermomechanical modelling of ice flow near the centre of large ice sheets with the finite-element technique. Ann. Glacial, 23,116123.
Mangeney, A. and Califano, F. 1998. The shallow ice approximation for anisotropic ice: formulation and limits. J. Geophys. Res., 103(B1), 691706.
Mangeney, A., Califano, F and Castelnau, O.. 1996. Isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide. J. Geophys. Res., 101 (B12), 28,18928,204.
Mangeney, A., Califano, F and Hutter, K.. 1997. A numerical study of anisotropic, low Reynolds number, free surface flow for ice sheet modeling. J. Geophys. Res., 102(B10), 22,74922,764.
Morland, L.W. 1984. Thermomechanical balances of ice sheet flows. Geophys. Astrophys. Fluid Dyn., 29, 237266.
Morland, L.W. and Johnson, I. R.. 1980. Steady motion of ice sheets. J. Glacial., 25(92), 229246.
Morland, L. and Staroszczyk, R.. 1998. Viscous response of polar ice with evolving fabric. Continuum Mech. Thermodyn., 10(3), 135152.
Pimienta, P., Duval, P. and Lipenkov, V.Ya. 1987. Mechanical behavior of anisotropic polar ice. International Association of Hydralogical Sciences Publication 170 (Symposium at Vancouver 1 9 8 7 - The Physical Basis of Ice Sheet Modelling), 5766.
Raymond, C. F 1983. Deformation in the vicinity of ice divides. J. Glacial., 29(103), 357373.
Staroszczyk, R. and Gagliardini, O.. 1999. Two orthotropic models for strain-induced anisotropy of polar ice. J. Glacial., 45 (151), 485494.
Staroszczyk, R. and Morland, L.W.. 2000. Orthotropic viscous response of polar ice. J. Eng Math., 37(1–3), 191209.
Zienkiewicz, O. C. and Taylor, R. L.. 1989. The finite element method. Vol. 1. Fourth edition. London, etc., McGraw-Hill Book Co.


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