Hostname: page-component-669899f699-b58lm Total loading time: 0 Render date: 2025-04-27T07:41:50.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Marine ice-sheet dynamics. Part 1. The case of rapid sliding

Published online by Cambridge University Press:  05 February 2007

CHRISTIAN SCHOOF
CHRISTIAN SCHOOF*
Affiliation:
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, V6T 1Z4, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Marine ice sheets are continental ice masses resting on bedrock below sea level. Their dynamics are similar to those of land-based ice sheets except that they must couple with the surrounding floating ice shelves at the grounding line, where the ice reaches a critical flotation thickness. In order to predict the evolution of the grounding line as a free boundary, two boundary conditions are required for the diffusion equation describing the evolution of the grounded-ice thickness. By analogy with Stefan problems, one of these conditions imposes a prescribed ice thickness at the grounding line and arises from the fact that the ice becomes afloat. The other condition must be determined by coupling the ice sheet to the surrounding ice shelves. Here we employ matched asymptotic expansions to study the transition from ice-sheet to ice-shelf flow for the case of rapidly sliding ice sheets. Our principal results are that the ice flux at the grounding line in a two-dimensional ice sheet is an increasing function of the depth of the sea floor there, and that ice thicknesses at the grounding line must be small compared with ice thicknesses inland. These results indicate that marine ice sheets have a discrete set of steady surface profiles (if they have any at all) and that the stability of these steady profiles depends on the slope of the sea floor at the grounding line.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 27 - 55
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Alley, R. B. & Bindschadler, R. A. (ed.) 2001 The West Antarctic Ice Sheet: Behaviour and Environment. American Geophysical Union, Washington, DC.CrossRefGoogle Scholar
Anandakrishnan, S., Voigt, D. E., Alley, R. B. & King, M. A. 2003 Ice stream flow speed is strongly modulated by the tide beneath the Ross Ice Shelf. Geophys. Res. Letts. 30, doi: 10.1029/2002GL016329.CrossRefGoogle Scholar
Bueler, E., Lingle, C. S., Kallen-Brown, J. A., Covey, D. N. & Bowman, L. N. 2005 Exact solutions and verification of numerical models for isothermal ice sheets. J. Glaciol. 51 (173), 291–306.CrossRefGoogle Scholar
Calvo, N., Díaz, J., Durany, J., Schiavi, E. & Vázquez, C. 2002 On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics. SIAM J. Appl. Maths 63, 683–707.CrossRefGoogle Scholar
Chugunov, V. A. & Wilchinsky, A. V. 1996 Modelling of marine glacier and ice-sheet–ice-shelf transition zone based on asymptotic analysis. Ann. Glaciol. 23, 59–67.CrossRefGoogle Scholar
Crank, J. 1984 Free and Moving Boundary Problems. Clarendon.Google Scholar
Dupont, T. K. & Alley, R. B. 2005a Assessment of the importance of ice-shelf buttressing to ice sheet flows. Geophys. Res. Letts. 32 (L04503), doi:10.1029/2004GL022024.CrossRefGoogle Scholar
Dupont, T. K. & Alley, R. B. 2005b Conditions for the reversal of ice/air surface slope on ice streams and ice shelves: a model study. Ann. Glaciol. 40, 139–144.CrossRefGoogle Scholar
Fowler, A. C. 1977 Glacier dynamics. PhD thesis, Oxford University.Google Scholar
Fowler, A. C. 1981 A theoretical treatment of the sliding of glaciers in the absence of cavitation. Phil. Trans. R. Soc. Lond. 298 (1445), 637–685.Google Scholar
Fowler, A. C. 1982 Waves on glaciers. J. Fluid Mech. 120, 283–321.CrossRefGoogle Scholar
Fowler, A. C. 1997 Mathematical Models in the Applied Sciences. Cambridge University Press.Google Scholar
Fowler, A. C. 2001 Modelling the flow of glaciers and ice sheets. In Continuum Mechanics and Applications in Geophysics and the Environment (ed. Straughan, B., Greve, R., Ehrentraut, H. & Wang, Y.), pp. 276–304. Springer.Google Scholar
Fowler, A. C. & Johnson, C. 1996 Ice-sheet surging and ice-stream formation. Ann. Glaciol. 23, 68–73.CrossRefGoogle Scholar
Fowler, A. C. & Larson, D. A. 1978 On the flow of polythermal glaciers. I. Model and preliminary analysis. Proc. R. Soc. Lond. A 363, 217–242.Google Scholar
Fowler, A. C. & Larson, D. A. 1980 The uniqueness of steady state flows in glaciers and ice sheets. Geophys. J. R. Astron. Soc. 63, 347–359.CrossRefGoogle Scholar
Herterich, K. 1987 On the flow within the transition zone between ice sheet and ice shelf. In Dynamics of the West Antarctic Ice Sheet. Proc. Workshop held in Utrecht, May 6–8, 1985 (ed. van der Veen, C. J. & Oerlemans, J.), pp. 185–202. D. Reidel.Google Scholar
Hindmarsh, R. C. A. 1996 Stability of ice rises and uncoupled marine ice sheets. Ann. Glaciol. 23, 94–104.CrossRefGoogle Scholar
Hindmarsh, R. C. A. 2006 The role of membrane-like stresses in determining the stability and sensitivity of the antarctic ice-sheets: back-pressure and grounding-line motion. Phil. Trans. R. Soc. Lond. A 364, 1733–1767.Google ScholarPubMed
Hindmarsh, R. C. A. & LeMeur, E. 2001 Dynamical processes involved in the retreat of marine ice sheets. J. Glaciol. 47 (157), 271–282.CrossRefGoogle Scholar
Hutter, K. 1983 Theoretical Glaciology. D. Reidel.CrossRefGoogle Scholar
Iverson, N. R., Baker, R. W., Hooke, R. LeB., Hanson, B. & Jansson, P. 1999 Coupling between a glacier and a soft bed: I. A relation between effective pressure and local shear stress determined from till elasticity. J. Glaciol. 45 (149), 31–40.CrossRefGoogle Scholar
LeMeur, E. & Hindmarsh, R. C. A. 2001 Coupled marine ice-sheet/earth dynamics using a dynamically consistent ice sheet and a self-gravitating viscous earth model. J. Glaciol. 47 (157), 258–270.Google Scholar
MacAyeal, D. R. 1987 Ice-shelf backpressure: form drag versus dynamics drag. In Dynamics of the West Antarctic Ice Sheet. Proc. Workshop held in Utrecht, May 6–8, 1985 (ed. van der Veen, C. J. & Oerlemans, J.), pp. 141–160. D. Reidel.Google Scholar
MacAyeal, D. R. 1989 Large-scale flow over a viscous basal sediment: theory and application to Ice Stream E, Antarctica. J. Geophys. Res. 94 (B4), 4017–4087.Google Scholar
MacAyeal, D. R. 1996 EISMINT: Lessons in Ice-Sheet Modeling. Tech. Rep. Department of Geophysical Sciences, University of Chicago, unpublished lecture notes.Google Scholar
MacAyeal, D. R. & Barcilon, V. 1988 Ice-shelf response to ice-stream discharge fluctuations: I. Unconfined ice tongues. J. Glaciol. 34 (116), 121–127.CrossRefGoogle Scholar
Morland, L. W. 1987 Unconfined ice-shelf flow. In Dynamics of the West Antarctic Ice Sheet. Proc. Workshop held in Utrecht, May 6–8, 1985 (ed. van der Veen, C. J. & Oerlemans, J.), pp. 99–116. D. Reidel.Google Scholar
Morland, L. W. & Johnson, I. R. 1980 Steady motion of ice sheets. J. Glaciol. 25 (92), 229–246.CrossRefGoogle Scholar
Muszynski, I. & Birchfield, G. E. 1987 A coupled marine ice-stream–ice-shelf model. J. Glaciol. 33 (113), 3–15.CrossRefGoogle Scholar
Nye, J. F. 2000 A flow model for the polar caps of Mars. J. Glaciol. 46 (154), 438–444.CrossRefGoogle Scholar
Oerlemans, J. 2002 Global dynamics of the Antarctic ice sheet. Climate Dyn. 19, 85–93.Google Scholar
Paterson, W. S. B. 1994 The Physics of Glaciers, 3rd edn. Pergamon.Google Scholar
Pattyn, F., Huyghe, A., De Brabander, S. & De Smedt, B. 2006 Role of transition zones in marine ice sheet dynamics. J. Geophys. Res. 111 (F02004), doi:10.1029/2005JF000394.Google Scholar
Schoof, C. 2004 On the mechanics of ice stream shear margins. J. Glaciol. 50 (169), 208–218.CrossRefGoogle Scholar
Schoof, C. 2005 The effect of cavitation on glacier sliding. Proc. R. Soc. Lond. A 461, 609–627, doi:10.1098/rspa.2004.1350.Google Scholar
Schoof, C. 2006a A variational approach to ice-stream flow. J. Fluid Mech. 556, 227–251.CrossRefGoogle Scholar
Schoof, C. 2006b Variational methods for glacier flow over plastic till. J. Fluid Mech. 555, 299–320.CrossRefGoogle Scholar
Shumskiy, P. A. & Krass, M. S. 1976 Mathematical models of ice shelves. J. Glaciol. 17, 419–432.CrossRefGoogle Scholar
Thomas, R. H. & Bentley, C. R. 1978 A model for Holocene retreat of the West Antarctic ice sheet. Quat. Res. 10, 150–170.CrossRefGoogle Scholar
Tulaczyk, S. 1999 Ice sliding over weak, fine-grained till: dependence of ice–till interactions on till granulometry. Spec. Paper Geol. Soc. Am. 337, 159–177.Google Scholar
Tulaczyk, S., Kamb, W. B. & Engelhardt, H. F. 2000 Basal mechanisms of Ice Stream B, West Antarctica: 2. Undrained plastic bed model. J. Geophys. Res. 105 (B1), 483–494.CrossRefGoogle Scholar
van der Veen, C. J. 1985 Response of a marine ice sheet to changes at the grounding line. Quat. Res. 24, 257–267.CrossRefGoogle Scholar
Vieli, A. & Payne, A. J. 2005 Assessing the ability of numerical ice sheet models to simulate grounding line migration. J. Geophys. Res. 110 (F01003), doi:10.1029/2004JF000202.Google Scholar
Weertman, J. 1974 Stability of the junction of an ice sheet and an ice shelf. J. Glaciol. 13 (67), 3–13.CrossRefGoogle Scholar
Weertman, J. 2005 Slip event propagation direction in transition region of low surface slope. Ann. Glaciol. 40, 43–46.CrossRefGoogle Scholar
Weis, M., Greve, R. & Hutter, K. 1999 Theory of shallow ice shelves. Cont. Mech. Thermodyn. 11, 15–50.CrossRefGoogle Scholar
Wilchinsky, A. V. 2001 Studying ice sheet stability using the method of separation of variables. Geophys. Astrophys. Fluid Dyn. 94, 15–45.CrossRefGoogle Scholar
Wilchinsky, A. V. & Chugunov, V. A. 2000 Ice stream-ice shelf transition: theoretical analysis of two-dimensional flow. Ann. Glaciol. 30, 153–162.CrossRefGoogle Scholar
Wilchinsky, A. V. & Chugunov, V. A. 2001 Modelling ice flow in various glacier zones. J. Appl. Maths Mech. 65, 479–493.CrossRefGoogle Scholar
Wilchinsky, A. V. & Feltham, D. L. 2004 Stability of an ice sheet on an elastic bed. Eur. J. Mech. B/Fluids 23, 681–694.CrossRefGoogle Scholar