Heat transport in stagnant lid convection with temperature- and pressure-dependent Newtonian or non-Newtonian rheology

Journal of Geophysical Research: Solid Earth

Volumn 104, Issue B6, 1999, Pages 12759-12777

  Dumoulin, Caroline ^a,b   Doin, Marie Pierre ^a,b   Fleitout, Luce ^a,b  

^a LABORATOIRE DE GÉOLOGIE   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT FLOW; LITHOSPHERE; NUMERICAL MODEL; VISCOSITY;

EID: 0033542320     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/1999jb900110     Document Type: Article

References (66)

1. Blundy, J. D., J. P. Brodholt, and B. J. Wood, Carbon-fluid equilibria and the oxidation state of the upper mantle, Nature, 349, 321-324, 1991.
2. Booker, J. R., Thermal convection with strongly temperature-dependent viscosity, J. Fluid Mech., 76, 741-754, 1976.
3. Castaing, B., G. Gunaratne, F. Heslot, L. Kadanoff, A. Libchaber, S. Thomae, X. Wu, S. Zaleski, and G. Zanetti, Scaling of hard thermal turbulence in Rayleigh-Bénard convection, J. Fluid Mech., 204, 1-30, 1989.
4. Christensen, U. R., Convection in a variable-viscosity fluid: Newtonian versus power-law rheology, Earth Planet. Sci. Lett., 64, 153-162, 1983.
5. Christensen, U. R., Convection with pressure- and temperature-dependent non-Newtonian rheology, Geophys. J. R. Astron. Soc., 77, 343-384, 1984a.
6. Christensen, U. R., Heat transport by variable viscosity convection and implications for the Earth's thermal evolution, Phys. Earth Planet. Inter., 35, 264-282, 1984b.
7. Christensen, U. R., Heat transport by variable viscosity convection, II, pressure influence, non-Newtonian rheology and decaying heat sources, Phys. Earth Planet. Inter., 37, 183-205, 1985.
8. Christensen, U. R., Mantle rheology, constitution and convection, in Mantle Convection, Plate Tectonics and Global Dynamics, edited by W. R. Peltier, pp. 595-655. Gordon and Breach, New York, 1989.
9. Christensen, U. R., and D. A. Yuen, Time dependent convection with non-Newtonian rheology, J. Geophys. Res., 94, 814-820, 1989.
10. Cserepes, L., Numerical studies of non-Newtonian mantle convection, Phys. Earth Planet. Inter., 30, 49-61, 1982.
11. Davaille, A., and C. Jaupart, Transient high-Rayleigh-number thermal convection with large viscosity variations, J. Fluid Mech., 253, 141-166, 1993.
12. Deschamps, F., Convection de Rayleigh-Bénard à viscosité variable: Applications géophysiques et planétologiques, Ph.D. thesis, 250 pp., Univ. Paris XI, 1997.
13. Doin, M. P., and L. Fleitout, Thermal evolution of the oceanic lithosphere: An alternative view, Earth Planet. Sci. Lett., 142, 121-136, 1996.
14. Doin, M.-P., L. Fleitout, and U. Christensen, Mantle convection and stability of depleted and undepleted continental lithosphere, J. Geophys. Res., 102, 2771-2787, 1997.
15. Dropkin, D., and E. Somerscales, Heat transfer by natural convection in liquids confined by two parallel plates which are inclined at various angles with respect to the horizontal, J. Heat Transfer, 87, 77-84, 1965.
16. Fjeldskaar, W., Viscosity and thickness of the asthenosphere detected from the Fennoscandian uplift, Earth Planet. Sci. Lett., 126, 399-410, 1994.
17. Fleitout, L., and D. Yuen, Secondary convection and the growth of oceanic lithosphere, Phys. Earth Planet. Inter., 36, 181-212, 1984a.
18. Fleitout, L., and D. Yuen, Steady state convection beneath lithospheric plates with temperature- and pressure-dependent viscosity, J. Geophys. Res., 89, 9227-9244, 1984b.
19. Fowler, A. C., Fast thermoviscous convection, Stud. Appl. Math., 72, 189-219, 1985.
20. Frick, H., F. H. Busse, and R. M. Clever, Steady three-dimensional convection at high Prandtl numbers, J. Fluid Mech., 127, 141-153, 1983.
21. Giannandrea, E., and U. Christensen, Variable viscosity convection experiments with a stress-free upper boundary and implications for the heat transport in the Earth's mantle, Phys. Earth Planet. Inter., 78, 139-152, 1993.
22. Goldstein, R. J., H. D. Chiang, and D. L. See, High-Rayleigh number convection in a horizontal enclosure, J. Fluid Mech., 213, 111-126, 1990.
23. Grasset, O., and E. M. Parmentier, Thermal convection in a volumetrically heated, infinite Prandtl number fluid with strongly temperature-dependent viscosity. Implications for planetary thermal evolution, J. Geophys. Res., 103, 18,171-18,181, 1998.
24. Hansen, U., and A. Ebel, Time-dependent thermal convection - A possible explanation for a multiscale flow in the Earth's mantle, Geophys. J., 94, 181-191, 1988.
25. Hansen, U., D. A. Yuen, and S. E. Kroening, Transition to hard turbulence in thermal convection at infinite Prandtl number, Phys. Fluids, A24, 2157-2163, 1990.
26. Hansen, U., D. A. Yuen, and A. V. Malevsky, Comparison of steady-state and strongly chaotic thermal convection at high Rayleigh number, Phys. Rev. A, 46, 4742-4754, 1992.
27. Hirth, G., and D. L. Kohlstedt, Water in the oceanic upper mantle: Implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Sci. Lett., 144, 93-108, 1996.
28. Honda, S., Local Rayleigh and Nusselt numbers for Cartesian convection with temperature-dependent viscosity, Geophys. Res. Lett., 23, 2445-2448, 1996.
29. Howard, L. N., Convection at high Rayleigh number, in Proceedings of the 11th International Congress on Applied Mechanics, edited by H. Gortler, pp. 1109-1115. Springer-Verlag, New York, 1964.
30. Jaoul, O., C. Froidevaux, W. B. Durham, and M. Michaut, Oxygen self-diffusion in Fosterite: Implications for the high-temperature creep mechanism, Earth Planet. Sci. Lett., 47, 391-397, 1980.
31. Jarvis, G. T., Time-dependent convection in the Earth's mantle, Phys. Earth Planet. Inter., 36, 305-327, 1984.
32. Jarvis, G. T., and W. R. Peltier, Mantle convection as a boundary layer phenomenon, Geophys. J. R. Astron. Soc., 68, 389-427, 1982.
33. Karato, S. I., and P. Wu, Rheology of the upper mantle: A synthesis, Science, 260, 771-778, 1993.
34. Kaufmann, G., and D. Wolf, Deglacial land emergence and lateral upper-mantle heterogeneity in the Svalbard Archipelago, II, Extended results for high-resolution load models, Geophys. J. Int., 127, 125-140, 1996.
35. Kraichnan, R. H., Turbulent thermal convection at arbitrary Prandtl number, Phys. Fluids, 5, 1374-1389, 1962.
36. Krishnamurti, R., and L. N. Howard, Large-scale flow generation in turbulent convection, Proc. Natl. Acad. Sci., 78, 1981-1985, 1981.
37. Lambeck, K., C. Smither, and P. Johnston, Sea-level change, glacial rebound and mantle viscosity for northern Europe, Geophys. J. Int., 134, 102-144, 1998.
38. Larsen, T. B., D. A. Yuen, A. V. Malevski, and A. J. Smedsmo, Dynamics of thermal convection with Newtonian temperature-dependent viscosity at high Rayleigh number, Phys. Earth Planet. Inter., 89, 9-33, 1995.
39. Larsen, T. B., D. A. Yuen, A. J. Smedsmo, and A. V. Malevski, Generation of fast timescale phenomena in thermo-mechanical processes, Phys. Earth Planet. Inter., 102, 213-222, 1997.
40. Moore, W. B., G. Schubert, and P. Tackley, Three-dimensional simulations of plume-lithosphere interaction at the Hawaiian swell, Science, 279, 1008-1011, 1998.
41. Moresi, L.-N., and V. S. Solomatov, Numerical investigation of 2D convection with extremely large viscosity variations, Phys. Fluids, 7, 2154-2162, 1995.
42. Morris, S., and D. Canright, A boundary-layer analysis of Bénard convection in a fluid of strongly temperature-dependent viscosity, Phys. Earth Planet. Inter., 36, 355-373, 1984.
43. Nataf, H. C., and F. M. Richter, Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets, Phys. Earth Planet. Inter., 29, 320-329, 1982.
44. Ogawa, M., G. Schubert, and A. Zebib, Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity, J. Fluid Mech., 233, 299-328, 1991.
45. Olson, P., A comparison of heat transfer laws for mantle convection at very high Rayleigh numbers, Phys. Earth Planet. Inter., 48, 153-160, 1987.
46. Parmentier, E. M., and J. Morgan, Thermal convection in non-Newtonian fluids: Volumetric heating and boundary layer scaling, J. Geophys. Res., 87, 7757-7762, 1982.
47. Parmentier, E. M., D. L. Turcotte, and K. E. Torrance, Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth's mantle, J. Geophys. Res., 81, 1839-1846, 1976.
48. Parmentier, E. M., C. Sotin, and B. J. Travis, Turbulent 3-D thermal convection in an infinite Prandtl number, volumetrically heated fluid: implications for mantle dynamics, Geophys. J. Int., 116, 241-251, 1994.
49. Parsons, B., and J. G. Sclater, An analysis of the variation of ocean floor bathymetry and heat flow with age, J. Geophys. Res., 82, 803-827, 1977.
50. Ranalli, G., The microphysical approach to mantle rheology, in Glacial Isostasy, Sea-Level and Mantle Rheology, edited by R. Sabadini, K. Lambeck, and E. Boschi, pp. 343-378. Kluwcr Acad., Norwell, Mass., 1991.
51. Ratcliff, J. T., G. Schubert, and A. Zebib, Three-dimensional variable viscosity convection of an infinite Prandtl number Boussinesq fluid in a spherical shell, Geophys. Res. Lett., 22, 2227-2230, 1995.
52. Ratcliff, J. T., G. Schubert, and A. Zebib, Steady tetrahedral and cubic patterns of spherical shell convection with temperature-dependent viscosity, J. Geophys. Res., 101, 25,473-25,484, 1996.
53. Ratcliff, J. T., P. J. Tackley, G. Schubert, and A. Zebib, Transitions in thermal convection with strongly variable viscosity, Phys. Earth Planet. Inter., 102, 201-212, 1997.
54. Reese, C., and V. Solomatov, Heat transport efficiency for stagnant lid convection with dislocation viscosity: Application to Mars and Venus, J. Geophys. Res., 103, 13,643-13,657, 1998.
55. Ricard, Y., and C. Vigny, Mantle dynamics with induced plate tectonics, J. Geophys. Res., 94, 17,543-17,559, 1989.
56. Roberts, G. O., Fast isoviscous Bénard convection, Geophys. Astrophys. Fluid Dyn., 12, 235-272, 1979.
57. Schubert, G., and C. A. Anderson, Finite element calculations of very high Rayleigh number thermal convection, Geophys. J. R. Astron. Soc., 80, 575-601, 1985.
58. Sigmundsson, F., Post-glacial rebound and asthenosphere viscosity in Iceland, Geophys. Res. Lett., 18, 1131-1134, 1991.
59. Sirovich, L., S. Balachandar, and M. R. Maxey, Simulations of turbulent thermal convection, Phys. Fluids, A12, 1911-1914, 1989.
60. Sleep, N. H., Lithospheric thinning by midplate mantle plumes and the thermal history of hot plume material ponded at sublithospheric depths, J. Geophys. Res., 99, 9327-9343, 1994.
61. Solomatov, V. S., Scaling of temperature- and stress-dependent viscosity convection, Phys. Fluids, 7, 266-274, 1995.
62. Solomatov, V. S., and L. N. Moresi, Three regimes of mantle convection with non-Newtonian viscosity and stagnant lid convection on the terrestrial planets, Geophys. Res. Lett., 24, 1907-1910, 1997.
63. Somerscales, E. F. C., and I. W. Gazda, Thermal convection in high Prandtl number liquids at high Rayleigh numbers, Rensselaer Polytech. Inst., ME Rep. HT-5. Troy, N. Y., 1968.
64. Stengel, K. C., D. S. Oliver, and J. R. Booker, Onset of convection in a variable viscosity fluid, J. Fluid Mech., 120, 411-431, 1982.
65. Turcotte, D. L., and E. R. Oxburgh, Finite amplitude convective cells and continental drifts, J. Fluid Mech., 28, 29-42, 1967.
66. Yuen, D. A., and L. Fleitout, Thinning of the lithosphere by small-scale convective destabilization, Nature, 313, 125-128, 1985.