Thermal convection in Earth's inner core with phase change at its boundary

Geophysical Journal International

Volumn 194, Issue 3, 2013, Pages 1310-1334

  Deguen, Renaud ^a   Alboussiére, Thierry ^b   Cardin, Philippe ^c  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UNIVERSITÉ LYON 1   (France)

^c UNIVERSITÉ GRENOBLE ALPES   (France)

Author keywords

Heat generation and transport; Instability analysis; Numerical solutions; Seismic anisotropy

Indexed keywords

ANALYTICAL EXPRESSIONS; HEAT GENERATION AND TRANSPORTS; INSTABILITY ANALYSIS; LATENT HEAT OF MELTING; LOW THERMAL CONDUCTIVITY; NUMERICAL SOLUTION; SEISMIC ANISOTROPY; SUPERADIABATIC TEMPERATURE;

COREMAKING; FREEZING; HEAT CONVECTION; MELTING; METAL MELTING; SOLIDIFICATION; VISCOSITY;

THERMAL CONDUCTIVITY;

FREEZING; HEAT TRANSFER; INNER CORE; INSTABILITY; LATENT HEAT FLUX; MELTING; RAYLEIGH NUMBER; SEISMIC ANISOTROPY; STABILITY ANALYSIS; STRATIFICATION; THERMAL CONDUCTIVITY; THERMAL CONVECTION; VISCOSITY;

EID: 84883026799     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1093/gji/ggt202     Document Type: Article

References (58)

1. Abramovich, M. & Stegun, I., 1965. Handbook of Mathematical Functions, Fourth Printing. Applied Math. Ser. 55, US Government Printing Office, Washington, DC.
2. Alboussière, T. & Ricard, Y., 2013. Reflections on dissipation associated with thermal convection, J. Fluid Mech., 725, doi:10.1017/jfm.2013.241.
3. Alboussière, T., Deguen, R. & Melzani, M., 2010. Melting induced stratification above the Earth's inner core due to convective translation, Nature, 466, 744-747.
4. Alfè, D., Gillan, M.J. & Price, G.D., 2002. Ab initio chemical potentials of solid and liquid solutions and the chemistry of the Earth's core, J. Chem. Phys., 116, 7127-7136.
5. Anderson, O.L. & Wenk Duba, A., 1997. Experimental melting curve of iron revisited, J. geophys. Res., 102, 22 659-22 670.
6. Anufriev, A., Jones, C. & Soward, A., 2005. The Boussinesq and anelastic liquid approximations for convection in the Earth's core, Phys. Earth planet. Inter., 12(3), 163-190.
7. Aubert, J., 2013. Flow throughout the Earth's core inverted from geomagnetic observations and numerical dynamo models, Geophys. J. Int., 192(2), 537-556.
8. Bergman, M., Lewis, D., Myint, I., Slivka, L., Karato, S. & Abreu, A., 2010. Grain growth and loss of texture during annealing of alloys, and the translation of Earth's inner core, Geophys. Res. Lett., 37(22), L22313, doi:10.1029/2010GL045103.
9. Buffett, B., 2009. Onset and orientation of convection in the inner core, Geophys. J. Int., 179, 711-719.
10. Buffett, B.A., 1997. Geodynamics estimates of the viscosity of the Earth's inner core, Nature, 388, 571-573.
11. Buffett, B.A. & Wenk, H.-R., 2001. Texturing of the Earth's inner core by Maxwell stresses, Nature, 413, 60-63.
12. Chandrasekhar, S., 1961. Hydrodynamic and Hydromagnetic Stability, International Series of Monographs on Physics, Clarendon, Oxford.
13. Christensen, U. & Aubert, J., 2006. Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetarymagnetic fields, Geophys. J. Int., 166(1), 97-114.
14. Cottaar, S. & Buffett, B., 2012. Convection in the Earth's inner core, Phys. Earth planet. Inter., 198-199, 67-78.
15. Davies, C.J., Silva, L. & Mound, J., 2013. On the influence of a translating inner core in models of outer core convection, Phys. Earth planet. Inter., 214, 104-114.
16. de Koker, N., Steinle-Neumann, G. & Vlcek, V., 2012. Electrical resistivity and thermal conductivity of liquid fe alloys at high p and t, and heat flux in earth's core, Proc. Natl. Acad. Sci., 109(11), 4070- 4073.
17. Deguen, R. & Cardin, P., 2011. Thermo-chemical convection in Earth's inner core, Geophys. J. Int., 187, 1101-1118.
18. Deguen, R., Cardin, P., Merkel, S. & Lebensohn, R., 2011. Texturing in Earth's inner core due to preferential growth in its equatorial belt, Phys. Earth planet. Inter., 188, 173-184.
19. Deschamps, F., Yao, C., Tackley, P.J. & Sanchez-Valle, C., 2012. High rayleigh number thermal convection in volumetrically heated spherical shells, J. geophys. Res.-Solid Earth, 117, E09006, doi:10.1029/2012JE004090.
20. Dziewonski, A.M. & Anderson, D.L., 1981. Preliminary reference Earth model, Phys. Earth planet. Inter., 25, 297-356.
21. Forte, A.M. & Peltier, W.R., 1987. Plate tectonics and aspherical Earth structure: the importance of poloidal-toroidal coupling, J. geophys. Res., 92, 3645-3679.
22. Geballe, Z.M., Lasbleis, M., Cormier, V.F. & Day, E.A., 2013. Sharp hemisphere boundaries in a translating inner core, Geophys. Res. Lett., 40, doi:10.1002/grl.50372.
23. Gillet, N., Pais, M.A. & Jault, D., 2009. Ensemble inversion of time-dependent core flow models, Geophys. J. Int., 10, Q06004, doi:10.1029/2008GC002290.
24. Gubbins, D., Masters, G. & Nimmo, F., 2008. A thermochemical boundary layer at the base of Earth's outer core and independent estimate of core heat flux, Geophys. J. Int., 174, 1007-1018.
25. Gubbins, D., Sreenivasan, B., Mound, J. & Rost, S., 2011. Melting of the Earth's inner core, Nature, 473(7347), 361-363.
26. Gubbins, D., Alfè, D. & Davies, D., 2013. Compositional instability of Earth's solid inner core, Geophys. Res. Lett., 40(1-5), 361-363.
27. Irving, J., Deuss, A. & Woodhouse, J., 2009. Normal mode coupling due to hemispherical anisotropic structure in Earth's inner core, Geophys. J. Int., 178(2), 962-975.
28. Jeanloz, R. & Wenk, H.-R., 1988. Convection and anisotropy of the inner core, Geophys. Res. Lett., 15, 72-75.
29. Karato, S.-I., 1999. Seismic anisotropy of the Earth's inner core resulting from flow induced by Maxwell stresses, Nature, 402, 871-873.
30. Koot, L. & Dumberry, M., 2011. Viscosity of the earth's inner core: constraints from nutation observations, Earth planet. Sci. Lett., 308(3-4), 343-349.
31. Mizzon, H.&Monnereau,M., 2013. Implications of the lopsided growth for the viscosity of Earth's inner core, Earth planet. Sci. Lett., 361, 391-401.
32. Monnereau, M., Calvet, M., Margerin, L. & Souriau, A., 2010. Lopsided growth of Earth's inner core, Science, 328, 1014-1017.
33. Mound, J.E. & Buffett, B.A., 2006. Detection of a gravitational oscillation in length-of-day, Earth planet. Sci. Lett., 243, 383-389.
34. Niu, F.L. & Wen, L.X., 2001. Hemispherical variations in seismic velocity at the top of the Earth's inner core, Nature, 410, 1081-1084.
35. Pais, A. & Jault, D., 2008. Quasi-geostrophic flows responsible for the secular variation of the Earth's magnetic field, Geophys. J. Int., 173, 421-443.
36. Parmentier, E.M. & Sotin, C., 2000. Three-dimensional numerical experiments on thermal convection in a very viscous fluid: implications for the dynamics of a thermal boundary layer at high Rayleigh number, Phys. Fluids, 12, 609-617.
37. Poirier, J.-P., 1994. Physical properties of the Earth's core, C.R. Acad. Sci. Paris, 318, 341-350.
38. Pozzo, M., Davies, C., Gubbins, D. & Alfè, D., 2012. Thermal and electrical conductivity of iron at Earth's core conditions, Nature, 485, 355- 358.
39. Reaman, D., Colijn, H., Yang, F., Hauser, A. & Panero, W., 2012. Interdiffusion of Earth's core materials to 65 GPa and 2200K, Earth planet. Sci. Lett., 349, 8-14.
40. Reaman, D.M., Daehn, G.S. & Panero, W.R., 2011. Predictive mechanism for anisotropy development in the Earth's inner core, Earth planet. Sci. Lett., 312(3-4), 437-442.
41. Ribe, N.M., 2007. Analytical approaches to mantle dynamics, in Treatise on Geophysics, pp. 167-226, eds Gerald, S. & Bercovici, D., Elsevier, New York.
42. Schubert, G., Turcotte, D.&Olson, P., 2001. Mantle Convection in the Earth and Planets, Cambridge University Press, Cambridge, UK.
43. Sha, X. & Cohen, R., 2011. First-principles studies of electrical resistivity of iron under pressure, J. Phys.: Conden. Matter, 23, 075401, doi:10.1088/0953-8984/23/7/075401.
44. Sneddon, I., 1960. On some infinite series involving the zeros of bessel functions of the first kind, in Proceedings of the Glasgow Mathematical Association, Vol. 4, pp. 144-156, Cambridge University Press, Cambridge, UK.
45. Souriau, A. & Poupinet, G., 1991. The velocity profile at the base of the liquid core from PKP(BC+Cdiff) data: an argument in favor of radial inhomogeneity, Geophys. Res. Lett., 18, 2023-2026.
46. Sreenivasan, B. & Gubbins, D., 2011. On mantle-induced heat flow variations at the inner core boundary, Phys. Earth planet. Inter, 187, 336- 341.
47. Stacey, F. & Loper, D., 2007. A revised estimate of the conductivity of iron alloy at high pressure and implications for the core energy balance, Phys. Earth planet. Inter., 161, 13-18.
48. Stacey, F.D. & Anderson, O.L., 2001. Electrical and thermal conductivities of Fe-Ni-Si alloy under core conditions, Phys. Earth planet. Inter., 124, 153-162.
49. Stacey, F.D.&Davis, P.M., 2008. Physics of the Earth, Cambridge University Press, Cambridge, UK.
50. Stevenson, D., 1987. Limits on lateral density and velocity variations in the Earth's outer core, Geophys. J. R. astr. Soc., 88(1), 311-319.
51. Sumita, I., Yoshida, S., Hamano, Y. & Kumazawa, M., 1995. A model for the structural evolution of the Earth's core and its relation to the observations, in The Earth's Central Part: Its Structure and Dynamics, pp. 231- 260, ed. Yukutake, T., Terra Scientific Publishing Company (Terrapub), Tokyo.
52. Tanaka, S., 2012. Depth extent of hemispherical inner core from pkp (df) and pkp (cdiff) for equatorial paths, Phys. Earth planet. Inter, 210-211, 50-62.
53. Tanaka, S. & Hamaguchi, H., 1997. Degree one heterogeneity and hemispherical variation of anisotropy in the inner core from PKP(BC)- PKP(DF) times, J. geophys. Res., 102, 2925-2938.
54. Tritton, D., 1988. Physical Fluid Dynamics, Clarendon Press, Oxford.
55. Van Orman, J.A., 2004. On the viscosity and creep mechanism of Earth's inner core, Geophys. Res. Lett., 31, L20606, doi:10.1029/2004GL021209.
56. Vočadlo, L., 2007. Ab initio calculations of the elasticity of iron and iron alloys at inner core conditions: evidence for a partiallymolten inner core?, Earth planet. Sci. Lett., 254, 227-232.
57. Weber, P.&Machetel, P., 1992. Convectionwithin the inner-core and thermal implications, Geophys. Res. Lett., 19, 2107-2110.
58. Yoshida, S., Sumita, I. & Kumazawa, M., 1996. Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy, J. geophys. Res., 101, 28 085-28 104.