Mantle convection models with temperature- and depth-dependent thermal expansivity

Journal of Geophysical Research: Solid Earth

Volumn 113, Issue 8, 2008, Pages

  Ghias, Sanaz R ^a   Jarvis, Gary T ^a,b  

^a YORK UNIVERSITY   (Canada)

^b YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT FLOW; HEAT FLUX; MANTLE CONVECTION; MODELING; TEMPERATURE PROFILE; THERMAL CONVECTION;

CALLUNA VULGARIS;

EID: 55949084356     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2007JB005355     Document Type: Article

References (71)

1. Anderson, O. L. (1981), Temperature profiles in the Earth, in Evolution of the Earth, Geodyn. Ser., vol. 5, edited by R. J. O'Connell and W. S. Fyfe, pp. 19-27, AGU Washington, D. C.
2. Anderson, O. L., H. Oda, and D. Issak (1992), A model for the computation of thermal expansivity at high temperature: MgO as an example, Geophys. Res. Lett., 19, 1987-1990, doi:10.1029 /92GL02145.
3. Balachandar, S., D. A. Yuen, and D. Reuteler (1992), Time-dependent three-dimensional compressible convection with depth-dependent properties, Geophys. Res. Lett., 19, 2247-2250, doi:10.1029/ 92GL02146.
4. Balachandar, S., D. A. Yuen, and D. M. Reuteler (1995a), Localization of toroidal motion and shear heating mi 3-D high Rayleigh number convection with temperature dependent viscosity, Geophys. Res. Lett., 22, 477-480, doi:10.1029/94GL03046.
5. Balachandar, S., D. A. Yuen, D. M. Reuteler, and G. S. Lauer (1995b), Viscous dissipation in three-dimensional convection with temperature-dependent viscosity, Science, 267, 1150-1153, doi:10.1126/science.267.5201.1150.
6. Boehler, R. (1996), Melting temperature of the Earth's mantle and core: Earth's thermal structure, Annu. Rev. Earth Planet. Sci., 24, 15-40, doi:10.1146/annurev.earth.24.1.15.
7. Booker, J. R. (1976), Thermal Convection with strongly temperature-dependent viscosity, J. Fluid Mech., 76, 741-754, doi:10.1017/S0022112076000876.
8. Booker, J. R., and K. C. Stengel (1978), Further thoughts on convective heat transport in a variable-viscosity fluid, J. Fluid Mech., 86, 289-291, doi:10.1017/80022112078001135.
9. Boussinesq, J. (1903), Théorie analytique de la Chaleur mise en, Harmonie avec la Thermodynamique et avec la mécanique de la Lumiére, vol. II, pp. 157-176, Gauthier-Villars, Paris.
10. Branland, J. M., M. C. Kameyama, D. A. Yuen, and Y. Kaneda (2000), Effects of temperature-dependent thermal diffusivity on shear instability in a viscoelastic zone: Implications for faster ductile faulting and earthquakes in the spinel stability field, Earth Planet. Sci. Lett., 182, 171-185, doi:10.1016/S0012-821X(00)00239-9.
11. Breuer, D., and T. Spohn (1993), Cooling of the Earth: Urey ratios, and the problem of potassium in the core, Geophys. Res. Lett., 20, 1655-1658, doi:10.1029/93GL01680.
12. Bunge, H. P., M. A. Richards, and J. R. Baumgardner (1996), Effects of depth-dependent viscosity on the planform of mantle convection, Nature, 379, 436-438, doi:10.1038/379436a0.
13. Butter, S. L., and G. T. Jarvis (2004), Stresses induced in continental lithospheres by axisymmetric spherical convection, Geophys. J. Int., 157, 1359-1376, doi:10.1111/j.1365-246X.2004.02257.x.
14. Butler, S. L., W. R. Peltier, and S. O. Costin (2005), Numerical models of the Earth's thermal history; Effects of inner-core solidification and core potassium, Phys. Earth Planet. Inter., 152, 22-42, doi:10.1016/j.pepi.2005.05.005.
15. Chandrasekhar, S. (1961), Hydrodynamic and hydromagnetic stability, Oxford Univ. Press, London.
16. Chopelas, A., and R. Boehler (1992), Thermal expansivity in the lower mantle, Geophys. Res. Lett., 19, 1983-1986, doi:10.1029/92GL02144.
17. Christensen, U. (1984), Convection with pressure- and temperature-dependent non-Newtonian rheology, Geophys. J. R. Astron. Soc., 77, 343-384.
18. Daly, S. F. (1980), The vagaries of variable viscosity convection, Geophys. Res. Lett., 7, 841-844, doi:10.1029/GL007i010p00841.
19. Davies, G. F. (1980), Thermal histories of convective Earth models and constraints on radiogenic heat-production in the Earth, J. Geophys. Res., 85, 2517-2530, doi:10.1029/JB085iB05p02517.
20. Doin, M. P., and L. Fleitout (1996), Thermal evolution of the oceanic lithosphere: An alternative view, Earth Planet. Sci. Lett., 142, 121-136, doi:10.1016/0012-821X(96)00082-9.
21. Fabrichnaya, O. B. (1999), The phase relations in the FeO-MgO-Al2O3-SiO2 system: Assessment of thermodynamic properties and phase equilibria at pressures up to 30 GPa, Calphad, 23(1), 19-67, doi:10.1016/ S0364-5916(99)00013-9.
22. Fei, Y. (1995), Thermal expansion, in Mineral Physics and Crystallography: A Handbook of Physical Constants, AGU Ref. Shelf, vol. 2, edited by T. J. Ahrens, pp. 29-44, AGU, Washington, D. C.
23. Ghias, S. R., and G. T. Jarvis (2007), Mantle flow reversals in cylindrical Earth models, Phys. Earth Planet. Inter, 165, 194-207, doi:10.1016/j.pepi.2007.09.004.
24. Gurnis, M. (1988), Large-scale mantle convection and aggregation and dispersal of supercontinents, Nature, 332, 695-699, doi:10.1038/ 332695a0.
25. Gurnis, M., and G. Davies (1986), Numerical study of high Rayleigh number convection in a medium with depth-dependent viscosity, Geophys. J. R. Astron. Soc., 85, 523-541.
26. Hansen, U., and D. A. Yuen,(1994), Effects of depth-dependent thermal expansivity on the interaction of thermal-chemical plumes with a compositional boundary, Phys Earth Planet. Inter., 86, 205-221, doi:10.1016/0031-9201(94)05069-4.
27. Hansen, U., D. A. Yuen, and S. E. Kroening (1991), Effects of depth-dependent thermal expansivity on mantle circulations and lateral thermal anomalies, Geophys. Res. Lett., 18, 1261-1264, doi:10.1029/91GL01288.
28. Hansen, U., D. A. Yuen, S. E. Kroening, and T. B. Larsen (1993), Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure, Phys. Earth Planet. Inter., 77, 205-223, doi:10.1016/0031-9201(93)90099-U.
29. Honda, S. (1995), A simple parameterized model of Earth's thermal history with the transition from layered to whole mantle convection, Earth. Planet. Sci. Lett., 131, 357-369, doi:10.1016/0012-821X (95)00034-A.
30. Israeli, M. (1970), A fast implicit numerical method for time-dependent viscous flows, Stud. Appl. Math., 49, 327-349.
31. Jarvis, G. T. (1993), Effects of curvature on two-dimensional models of mantle convection: Cylindrical polar coordinates, J. Geophys. Res., 98, 4477-4485, doi:10.1029/92JB02117.
32. Jarvis, G. T., and J. P. Lowman (2007), Survival times of subducted slab remnants in numerical models of mantle flow, Earth Planet. Sci. Lett., 260, 23-36, doi:10.1016/j.epsl.2007.05.009.
33. Jarvis, G. T., and D. P. McKenzie (1980), Convection in a compressible fluid with infinite Prandtl number, J. Fluid Mech., 96, 515-583, doi:10.1017/S002211208000225X.
34. Jarvis, G. T., and W. R. Peltier (1982), Mantle convection as a boundary layer phenomenon, Geophys. J. R. Astron. Soc., 68, 389-427.
35. Jeffreys, H. (1930), The instability of a compressible fluid heated below, Proc. Cambridge Philos. Soc., 26, 170-172.
36. Koglin, D. E., Jr., S. R. Ghias, S. D. King, G. T. Jarvis, and J. P. Lowman (2005), Mantle convection with reversing mobile plates: A benchmark study, Geochem. Geophys. Geosyst., 6, Q09003, doi:10.1029/2005GC000924.
37. Lowman, J. P., and G. T. Jarvis (1993), Mantle convection flow reversals due to continental collisions, Geophys. Res. Lett., 20, 2087-2090, doi:10.1029/93GL02047.
38. Lowman, J. P., and G. T. Jarvis (1995), Mantle convection models of continental collision and breakup incorporating finite thickness plates, Phys. Earth. Planet. Inter., 88, 53-68, doi:10.1016/0031-9201 (94)05076-A.
39. Lowman, J. P., and G. T. Jarvis (1999), Effects of mantle heat source distribution on supercontinent stability, J. Geophys. Res., 104, 12,733-12,746, doi:10.1029/1999JB900108.
40. Matyska, C., and D. A. Yuen (N06), Lower mantle dynamics with the post-perovskite phase change, radiative thermal conductivity, temperature- and depth-dependent viscosity, Phys. Earth Planet. Inter., 154, 196-207, doi:10.1016/j.pepi.2005.10.001.
41. McKenzie, D. P., and N. O. Weiss (1980), The thermal history of the Earth, in The Continental Crust and Its Mineral Deposits, edited by D. W. Strangway, Spec. Pap. Geol. Assoc. Can., 20 575-590.
42. McKenzie, D. P., J. M. Roberts, and N. O. Weiss (1974), Convection in the Earth's mantle: Towards a numerical simulation, J. Fluid Mech., 62, 465-538, doi:10.1017/S0022112074000784.
43. Mitrovica, J. X., and G. T. Jarvis (1987), A numerical study of thermal convection between rigid horizontal boundaries, Geophys. Astrophys. Fluid Dyn., 38, 193-224, doi:10.1080/03091928708219204.
44. Monnereau, M., and D. A. Yuen (2007), Topology of the postperovskite phase transition and mantle dynamics, Proc. Natl. Acad. Sci. U. S. A., 104, 9156-9161, doi:10.1073/pnas.0608480104.
45. Moore, D. R., and N. O. Weiss (1973), Two dimensional Rayleigh-Benard convection, J. Fluid Mech., 58, 289-312, doi:10.1017/ S0022112073002600.
46. Nataf, H. C., and F. M. Richter (1982), Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets, Phys. Earth Planet. Inter., 29, 320-329, doi:10.1016/ 0031- 9201(82)90020-6.
47. Nimmo, F., G. D. Price, J. Brodholt, and D. Gubbins (2004), The influence of potassium on core and geodynamo evolution, Geophys. J. Int., 156, 363-376, doi:10.1111/j.1365-246X.2003.02157.x.
48. Ogawa, M., G. Schubert, and A. Zebib (1991), Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity, J. Fluid Mech., 233, 299-328, doi:10.1017/S0022112091000496.
49. Richter, F. M. (1973), Dynamical models for sea floor spreading, Rev. Geophys., 11, 223-287, doi:10.1029/RG011i002p00223.
50. Saxena, S. K., N. Chatterjee, Y. Fei, and G. Shen (1993), Thermodynamic Data on Oxides and Silicates, Springer, Berlin.
51. Schmeling, H., G. Marquart, and T. Ruedas (2003), Pressure- and temperature- dependent thermal expansivity and the effect on mantle convection and surface observables, Geophys. J. Int., 154, 224-229, doi:10.1046/j.1365-246X.2003.01949.x.
52. Schubert, G., P. Cassen, and R. E. Young (1979), Subsolidus convection cooling histories of terrestrial planets, Icarus, 38, 192-211, doi:10.1016/0019-1035(79)90178-7.
53. Schubert, G., D. Stevenson, and P. Cassen (1980), Whole planet cooling and the radiogenic heat-source contents of the Earth and Moon, J. Geophys. Res., 85, 2531-2538, doi:10.1029/JB085iB05p02531.
54. Schubert, G., D. L. Turcotte, and P. Olson (Eds.) (2001), Mantle Convection in the Earth and planets, Cambridge Univ. Press, Cambridge, U. K.
55. Sharpe, H. N., and W. R. Peltier (1978), Parameterized mantle convection and the Earth's thermal history, Geophys. Res. Lett., 5, 737-740, doi:10.1029/GL005i009p00737.
56. Sharpe, H. N., and W. R. Peltier (1979), A thermal history model for the Earth with parameterized convection, Geophys. J. R. Astron. Soc., 59, 171-203.
57. Solheim, L., and W. R. Peltier (1990), Heat transfer and the onset of chaos in a spherical, axisymmetric, anelastic model of whole mantle convection, Geophys. Astrophys. Fluid Dyn., 53, 205-255, doi:16.1080/03091929009208928.
58. Stacey, F. D. (1977), A thermal model of the Earth, Phys. Earth Planet. Inter., 15, 341-348, doi:10.1016/0031-9201(77)90096-6.
59. Stacey, F. D. (1978), Possibility of a geophysical determination of the Newtonian gravitational constant, Geophys. Res. Lett., 5, 377-378, doi:10.1029/GL005i005p00377.
60. Stein, C., J. Schmalzl, and U. Hansen (2004), The effects of rheologica parameters on plate behaviour in a self-consistent model of mantle convection, Phys. Earth Planet, Inter., 142, 225-255, doi:10.1016/ j.pepi.2004.01.006.
61. Steinberger, B., and A. R. Calderwood (2006), Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations, Geophys. J. Int., 167, 1461-1481, doi:10.1111/j.136-246X.2006.03131.x.
62. Stemmer, K., H. Harder, and U. Hansen (2006), A new method to simulate convection with strongly temperature- and pressure-dependent viscosity in a spherical shell: Applications to the Earth's mantle, Phys. Earth Planet. Inter., 157, 223-249, doi:10.1016/j.pepi.2006,04.007.
63. Tackley, P. J. (1993), Effects of strongly temperature dependent viscosity on time-dependent, three-dimensional models of mantle convection, Geophys. Res. Lett., 20, 2187-2190, doi:10.1029/ 93GL02317.
64. Tackley, P. J. (1996), Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles, J. Geophys. Res., 101, 3311-3332, doi:10.1029/95JB03211.
65. Torrance, K. E., and D. L. Turcotte (1971), Structure of convection cells in the mantle, J. Geophys. Res., 76, 1154-1161, doi:10.1029/ JB076i005p01154.
66. Turcotte, D. L., and E. R. Oxburgh (1967), Finite amplitude convection cells and continental drift, J. Fluid Mech., 28, 29-42, doi:10.1017/S0022112067001880.
67. Van den Berg, A. P., D. A. Yuen, and J. R. Allwardt (2002), Non-linear effects from variable thermal conductivity and mantle internal heating: Implications for massive melting and secular cooling of the mantle, Phys Earth Planet. Inter., 129, 359-375, doi:10.1016 /S0031-9201(01) 00304-1.
68. Vangelov, V. I., and G. T. Jarvis (1994), Geometrical effects of curvature in axisymmetric spherical models of mantle convection, J. Geophys. Res., 99, 9345-9358, doi:10.1029/93JB03133.
69. van Keken, P. (2001), Cylindrical scaling for dynamical cooling models of the Earth, Phys. Earth Planet. Inter., 124, 119-130, doi:10.1016/S0031- 9201(01)00195-9.
70. Zhang, S., and D. A. Yuen (1995), The influence of lower mantle viscosity stratification on 3D spherical-shell mantle convection, Earth Planet. Sci. Lett., 132, 157-166, doi:10.1016/ 0012-821X(95)00038-E.
71. Zhao, W., and D. A. Yuen (1987), The effects of adiabatic and viscous heatings on plumes, Geophys. Res. Lett., 14, 1223-1226, doi:10.1029/GL014i012p01223.