Theory of Floating Ice Sheets

  • K. Hutter
  • F. M. Williams
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


In ice sheets, extensions in horizontal direction are very much larger than perpendicular to it, suggesting a two-dimensional approximate analysis. It is indicated how the usual plate models for stress analyses can be derived from general approximating techniques, and how two-dimensional descriptions for thermo-mechanical interactions in floating ice sheets are obtained. A “plate model” for the thermal response of an ice shelf is thus derived. The governing equations include accumulation at the top and phase change at the bottom and take convection and dissipation into account. An analysis of the steady state response is presented, and the response of the shelf to climatic conditions is determined. Generalizations to time-dependent situations are indicated.


Classical Plate Theory Shelf Thickness Couple Field Equation Orthogonal Function Expansion Weighted Thickness Average 
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  1. 1.
    Mindlin, R.D.; Medick, M.A.: Extensional vibrations of elastic plates. J. Applied Mechanics. 26 (1959).Google Scholar
  2. 2.
    Naghdi, P.M.: The Theory of Shells and Plates. Handbuch der Physik, Vol VIa/2. Berlin, Göttingen, Heidelberg: Springer 1972.Google Scholar
  3. 3.
    Hutter, K.: On the fundamental equations of floating ice. Mitteilung der Versuchsanstalt für Wasserbau, Hydrologie und Glaciology, ETH Zürich. 8 (1973) 1–150.MathSciNetGoogle Scholar
  4. 4.
    Hertz, H. Ueber das Gleichgewicht schwimmender elastischer Platten. Widemanns Annalen der Physik und Chemie. 22 (1884) 449–455.ADSCrossRefGoogle Scholar
  5. 5.
    Nevel, D.E.: Creep theory for a floating ice sheet. Special Report 76–4. Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire (1976) 1–98.Google Scholar
  6. 6.
    Kerr, A.D.: The bearing capacity of floating ice plates subjected to static or quasistatic loads. Journal of Glaciology, 17 (1976) 229–268.ADSGoogle Scholar
  7. 7.
    Assur, A.: Flexural and other properties of sea ice sheets. Proc. Conf. Inst. Low. Temp. Sc. Hokkaido Univ. (1966).Google Scholar
  8. 8.
    Kerr, A.D.; Palmer, W.T.: The deformations of stresses in floating ice plates. Acta Mechanica, 15 (1972) 57–72.MATHCrossRefGoogle Scholar
  9. 9.
    Hutter, K.: Floating sea ice plates and the significance of the dependence of the Poisson ratio on brine content. Proc. Royal. Soc. A 343 (1975) 85–105.ADSCrossRefGoogle Scholar
  10. 10.
    Williams, F.M.: Time dependent deflections of non- homogeneous ice plates. Acta Mechanica. 25 (1976) 29–44.MATHCrossRefGoogle Scholar
  11. 11.
    Hutter, K: On the mechanics of floating ice sheets. Mitteilung der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zürich. 28 (1978) 1–103.Google Scholar
  12. 12.
    Weertman, J.: Deformation of floating ice shelves. Journal of Glaciology, 3. (1957) 38–42.ADSGoogle Scholar
  13. 13.
    Thomas, R.H.: The creep of ice shelves: Theory. Journal of Glaciology. 12 (1973) 45–53.ADSGoogle Scholar
  14. 14.
    Robin, Q.: Ice movement and temperature distribution in glaciers and ice sheets. Journal of Glaciology, 2 (1955) 523–532.ADSCrossRefGoogle Scholar
  15. 15.
    Weertman, J.: Mechanism for the formation of inner moraines found near the edge of cold ice caps and ice sheets. Journal of Glaciology, 3 (1961) 975–978.ADSGoogle Scholar
  16. 16.
    Zotikov, I.A.: Bottom melting in the central zone of the shield on the antarctic continent and its influence upon the present balance of the ice mass. Bulletin Int. Ass. Sc. Hydr. 8 (1963) 36–44.CrossRefGoogle Scholar
  17. 17.
    Grigoryan, S.S.; Krass, M.S.; Shumskiy, P.A.: Mathematical model of a three-dimensional non-isothermal glacier. Journal of Glaciology, 17 (1976) 401–417.ADSGoogle Scholar
  18. 18.
    Shumskiy, P.A.; Krass, M.S.: Mathematical models of ice shelves. Journal of Glaciology 17 (1976) 419–432.ADSGoogle Scholar
  19. 19.
    Rektorys, R. (editor): Survey in Applicable Mathematics. Translation from the Russian. Boston: The MIT Press 1969.Google Scholar
  20. 20.
    Williams, F.M.; Hutter, K.: On the temperature distribution in harmonically excited thermoviscoelastic plates. In preparation.Google Scholar
  21. 21.
    Williams, F.M.; Hutter, K.: Thermal response of ice shelves to climatic conditions. In preparation.Google Scholar
  22. 22.
    Thomas, R.H.: The creep of ice shelves: Interpretation of observed behaviour. Journal of Glaciology. 12 (1973) 55–70.ADSMATHGoogle Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1980

Authors and Affiliations

  • K. Hutter
    • 1
  • F. M. Williams
    • 1
  1. 1.Laboratory of Hydraulics, Hydrology and GlaciologyFederal Institute of TechnologyZürichSwitzerland

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