Skip to main content
SpringerLink
Log in

Coupled velocity and temperature fields: the ice-sheet problem

  • Chapter
Very Slow Flows of Solids

Part of the book series: Mechanics of Fluids and Transport Processes ((MFTP,volume 7))

  • 162 Accesses

Abstract

The coupling between velocity and temperature fields is multiple. The flow acts on the temperature in two ways:

  1. (1)

    It allows heat advection (cf. Chapter 2).

  2. (2)

    It produces a viscous dissipation of heat.

The temperature acts on the flow in two ways:

  1. (3)

    The viscosity is temperature-dependent. The first sections of this chapter consider the effects (2) and (3) only; next, to model an ice-sheet, effect (1) will be added.

  2. (4)

    Thermal dilatation produces buoyancy forces, that may allow thermal convection, i.e., flow in a bounded domain without any input of mechanical energy. The next chapter is devoted to this problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. -P. Poirier, J. -L. Bouchez and J. J. Jonas: A dynamic model for aseismic ductile shear zones, Earth Planet. Sci. Letters, 43 (1979) pp. 441–453.

    Article  Google Scholar 

  2. L. Lliboutry: Tectonophysique et Géodynamique, Masson, Paris (1982), p. 279.

    Google Scholar 

  3. C. Froidevaux and G. Schubert: Plate motion and structure of the continental asthenosphere: a realistic model of the upper mantle, J. Geophys. Res., 80 (1975) pp. 2553–2564.

    Article  Google Scholar 

  4. D. L. Turcotte and E. R. Oxburgh: Mantle convection and the new Global Tectonics, Ann. rev. fluid mechanics, 4 (1972) pp. 33–68.

    Article  Google Scholar 

  5. J. -M. Vanpé: Contribution à l’étude du manteau dans le voisinage d’une plaque de lithosphère plongeante, Thèse de spécialité, Univ. of Grenoble I (1979).

    Google Scholar 

  6. G. Schubert, D. A. Yuen, C. Froidevaux, L. Fleitout and M. Souriau: Mantle circulation with partial shallow return flow, J. Geophys. Res., 81 (1978) pp. 745–758.

    Article  Google Scholar 

  7. W. von Hofmann: Die Internationale Glaziologische Grönland Expedition (EGIG), Z. für Gletscherkunde Glazialgeol, 10 (1974) pp. 217–224.

    Google Scholar 

  8. W. F. Budd, D. Jenssen and U. Radok: Derived physical characteristics of the Antarctic ice-sheet, Meteorology Dept., Univ. of Melbourne, Publ. No. 18 (1971).

    Google Scholar 

  9. W. F. Budd, T. H. Jacka, D. Jenssen, U. Radok and N. W. Young: Derived physical characteristics of the Greenland ice-sheet, Meteorology Dept., Univ. of Melbourne, Publ. No. 23 (1982).

    Google Scholar 

  10. W. J. Campbell and L. A. Rasmussen: A heuristic numerical model for three-dimensional time-dependent glacier flow. In: Symp. on Antarctic Glaciological Exploration (ISAGE), Hanover, N.H., 3–7 Sept. 1968, IAHS Publ. No. 86 (1970) pp. 177–190.

    Google Scholar 

  11. M. Abramowitz and I. A. Stegun (eds.): Handbook of mathematicalfunctions with formulas, graphs, and mathematical tables, Dover Publ. Inc., New York, p. 319.

    Google Scholar 

  12. D. Jenssen and U. Radok: Heat conduction in thinning ice sheets, J. Glaciol., 4 (1963) pp. 387–397.

    Google Scholar 

  13. W. F. Budd, D. Jenssen and N. W. Young: Temperature and velocity interaction in the motion of ice sheets. In: First Australian Conference on heat and mass transfer, Monash Univ., Melbourne (1973) pp. 17–24.

    Google Scholar 

  14. W. Dansgaard and S. J. Johnsen: A flow model and a time scale for the ice core from Camp Century, Greenland, J. Glaciol., 8 (1969) pp. 215–223.

    Google Scholar 

  15. C. U. Hammer, H. B. Clausen, W. Dansgaard, N. Gundestrup, S. J. Johnsen and N. Reeh: Dating of Greenland ice cores by flow models, isotopes, volcanic debris, and continental dust, J. Glaciol., 20 (1978) pp. 3–26.

    Google Scholar 

  16. K. Philberth and B. Fédérer: On the temperature profile and the age profile in the central part of cold ice sheets, J. Glaciol., 10 (1971) pp. 3–14.

    Google Scholar 

  17. C. Ritz, L. Lliboutry and C. Rado: Analysis of a 870 m deep temperature profile at Dome C, Annals of Glaciology, 3 (1982) pp. 284–289.

    Google Scholar 

  18. L. Lliboutry: A critical review of analytical approximate solutions for steady state velocities and temperatures in cold ice sheets, Z für Gletscherkunde Glazialgeol, 15 (1979) pp. 135–148.

    Google Scholar 

  19. R. Thorn: Structural stability and morphogenesis, W. A. Benjamin, New York (1975).

    Google Scholar 

  20. K. Hutter: Theoretical glaciology, D. Reidel, Dordrecht/Terra Sci. Publ. Co., Tokyo (1983).

    Google Scholar 

  21. J. A. Dowdeswell, D. J. Drewry, O. Liestol and O. Ohreim: Radio-echo sounding of Spitsbergen glaciers: problems in the interpretation of layer and bottom returns, J. Glaciol., 30 (1984) pp. 3–15.

    Google Scholar 

  22. L. Lliboutry: Bottom temperatures and basal low-velocity layer in an ice-sheet, J. Geophys. Res., 71 (1966) pp. 2535–2543. Correction, ibid. p. 6152.

    Google Scholar 

  23. D. A. Yuen and G. Schubert: The role of shear heating in the dynamics of large ice masses, J. Glaciol., 24 (1979) pp. 195–212.

    Google Scholar 

  24. A. C. Fowler and D. A. Larson: The uniqueness of steady state flows of glaciers and ice-sheets, Geophys. J. Roy. astron. Soc., 63 (1980) pp. 333–345. Thermal stability properties of a model of glacier flow, ibid., pp. 347–359

    Google Scholar 

  25. G. K. C. Clarke, U. Nitsan and W. S. B. Paterson: Strain heating and creep instability in glaciers and ice sheets, Rev. Geophys. Space Phys., 15 (1977) pp. 235–247.

    Article  Google Scholar 

  26. L. Lliboutry, Traité de Glaciologie. Vol 2: Glaciers, variations du climat, sols gelés, Masson & Cie., Paris (1965) pp. 770–785.

    Google Scholar 

  27. C. Lorius, J. Jouzel, C. Ritz, L. Merlivat, N. I. Barkov, Y. S. Korotkevich and V. M. Kotlyakov: A 150,000 year climatic record from Antarctic ice, Nature, 316 (1985) pp. 591–596.

    Article  Google Scholar 

  28. R. Peltier: Dynamics of the Ice Age Earth. In: Advances in Geophysics, Academic Press, New York, 24 (1982) pp. 1–146.

    Google Scholar 

  29. G. E. Birchfield, J. Weertman and A. T. Lunde: A model study of the role of high-latitude topography in the climatic response to orbital insolation anomalies, J. Atmosph. Sci., 39 (1982) pp. 71–87.

    Article  Google Scholar 

  30. M. Ghil and H. Le Treut: A climate model with cryodynamics and geodynamics, J. Geophys. Res., 86, No. C6 (1981) pp. 5262–5270.

    Article  Google Scholar 

  31. J. Oerlemans: Modeling of Pleistocene European ice sheets: some experiments with simple mass-balance parameterizations, Quaternary Res., 15 (1981) pp. 77–85.

    Article  Google Scholar 

  32. D. Pollard: A simple ice-sheet model yields realistic 100 kyr glacial cycles, Nature, 296 (1982) pp. 334–338.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Grenoble I, Grenoble, France

    Louis A. Lliboutry (Professor of Geophysics)

Authors
  1. Louis A. Lliboutry
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Martinus Nijhoff Publishers, Dordrecht

About this chapter

Cite this chapter

Lliboutry, L.A. (1987). Coupled velocity and temperature fields: the ice-sheet problem. In: Very Slow Flows of Solids. Mechanics of Fluids and Transport Processes, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3563-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3563-1_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8094-1

  • Online ISBN: 978-94-009-3563-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation