On shear flow of a saturated ice-sediment mixture with thermodynamic equilibrium pressure and momentum exchange

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 454, Issue 1968, 1998, Pages 71-88

  Wu, T ^a   Hutter, K ^a   Svendsen, B ^a,b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b BAM FEDERAL INSTITUTE FOR MATERIALS RESEARCH AND TESTING   (Germany)

Author keywords

Finite strain theory; Gravity driven flow; Ice flow; Ice sediment mixture; Saturated mixture; Thermodynamic consistent formulation

Indexed keywords

EID: 0010416186     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0147     Document Type: Article

References (30)

1. Alley, R. B., Blankenship, D. D., Bentley, C. R. & Rooney, S. T. 1987a Till beneath ice stream B. 3. Till deformation: Evidence and implications. J. Geophys. Res. 92, 8921-8929.
2. Alley, R. B., Blankenship, D. D., Rooney, S. T. & Bentley, C. R. 1987b Till beneath ice stream B. 4. A coupled ice-till flow model. J. Geophys. Res. 92, 8931-8940.
3. Birch, F. 1952 Elasticity and constitution of the Earth's interior. J. Geophys. Res. 57, 227-286.
4. Blankenship, D. D., Bentley, C. R., Rooney, S. T. & Alley, R. B. 1987 Till beneath ice stream B. 1. Properties derived from seismic travel times. J. Geophys. Res. 92, 8903-8911.
5. Boulton, G. S. & Hindmarsh, R. C. A. 1987 Sediment deformation beneath glaciers: rheology and geological consequences. J. Geophys. Res. 92, 9059-9082.
6. Clarke, G. K. C. 1987 Subglacial till: a physical framework for its properties and processes. J. Geophys. Res. 92, 9023-9036.
7. Dahl-Jensen, D. 1985 Determination of the flow properties of Dye 3, South Greenland, by borehole tilting measurements and perturbation modelling. J. Glaciol. 31, 92-98.
8. Drew, D. A. & Segel, L. A. 1971 Averaged equations for two-phase flows. Studies Appl. Math. L, 205-231.
9. Engelhardt, H. F., Harrison, W. D. & Kamb, B. 1978 Basal sliding conditions at the glacier bed as revealed by borehole photography. J. Glaciol. 20, 469-508.
10. Hutter, K. & Engelhardt, H. F. 1988a How useful is continuum thermodynamics to formulate concepts of ice sheet dynamics? Mitt, der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie. Eidg. Techn. Hochschule Zürich, Nr. 91, 163-210.
11. Hutter, K. & Engelhardt, H. F. 1988b The use of continuum thermodynamics in the formulation of ice-sheet dynamics. Ann. Glacial. 11, 46-51.
12. Hutter, K., Jöhnk, K. & Svendsen, B. 1994 On interfacial transition conditions in two-phase gravity flow. Z. Angew. Math. Phys. 45, 746-762.
13. Johnsen, S. J. & Dansgaard, W. 1992 On flow model dating of stable isotope records from Greenland ice cores. The last deglaciation: absolute and radiocarbon chronologies (ed. E. Bard & W. S. Broecker), vol. 12, NATO ASI Series. Berlin: Springer.
14. Jöhnk, K., Hutter, K. & Svendsen, B. 1993 Steady-state gravity flow of a binary mixture down an incline plane. Recent Advances in the Mechanics of Structured Continua, AMD vol. 160/MD-vol. 41, pp. 55-63. New York: ASME.
15. Leliwa-Kopystynski, J. & Teisseyre, R. 1984 Physics and evolution of the Earth's interior 1. Constitution of the Earth's interior. Elsevier; Warszawa: PWN-Polish Scientific.
16. Love, A. E. H. 1927 A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press.
17. Liu, I.-S. 1972 Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Ration. Mech. Analysis 46, 131-148.
18. MacKenzie, D. 1984 The generation and compaction of partially molten rock. J. Petrology 25, 713-765.
19. Murnaghan, F. D. 1951 Finite deformation of an elastic solid. New York: Wiley.
20. Nunziato, J. W. 1983 A multiphase mixture theory for fluid-particle flows. In Theory of dispersed multiphase flow (ed. R. E. Meyer), pp. 191-226. New York: Academic.
21. Passman, S. L., Nunziato, J. W. & Walsh, E. K. 1984 A theory of multiphase mixtures. In Rational thermodynamics (ed. C. Truesdell). Berlin: Springer.
22. Rooney, S. T., Blankenship, D. D., Alley, R. B. & Bentley, C. R. 1987 Till beneath ice stream B. 2. Structure and continuity. J. Geophys. Res. 92, 8913-8920.
23. Stacey, F. D., Brennan, B. J. & Irvine, R. D. 1981 Finite strain theories and comparisons with seismological data. Geophysical Surveys 4, 189-232.
24. Svendsen, B. & Hutter, K. 1995 On the thermodynamics of a mixture of viscous fluids with constraints. Int. J. Eng. Sci. 33, 2021-2054.
25. Svendsen, B., Wu, T., Jöhnk, K. & Hutter, K. 1996 On the role of mechanical interactions in the steady-state gravity flow of a two-constituent mixture down an inclined plane. Proc. R. Soc. Lond. A 452, 1189-1205.
26. Truesdell, C. 1984 Rational thermodynamics. Berlin: Springer.
27. Vulliet, L. & Hutter, K. 1988 Continuum model for natural slopes in slow movement. Géotechnique 38, 199-217.
28. Wu, T. 1996 Schwerkraftgetriebene Scherströmungen in gesättigen Binärmischungen nicht-Newtonscher Fluide mit Anwendungen auf das Fließen von sedimentverschmutztem Eis. Ph.D. thesis, Technische Hochschule Darmstadt. Schaker Verlag Aachen.
29. Wu, T. & Hutter, K. 1998 On the role of the interface mechanical interaction in a gravity-driven shear flow of an ice-till mixture. Porous Media. (Submitted.)
30. Wu, T., Jöhnk, K., Svendsen, B. & Hutter, K. 1996 On the gravity-driven shear flow of an ice-till mixture. Ann. Glacial. 23, 359-363.