Arkani-Hamed, J., Effects of the core cooling on the internal dynamics and thermal evolution of terrestrial planets, J. Geophys. Res., 99, 12109–12119, 1994.
Article
Google Scholar
Christensen, U. R., Heat transport by variable viscosity convection and implications for the Earth’s thermal evolution, Phys. Earth Planet. Inter., 35, 264–282, 1984.
Article
Google Scholar
Christensen, U. R., Thermal evolution models for the earth, J. Geophys. Res., 90, 2995–3007, 1985.
Article
Google Scholar
Davies, G. F., Thermal histories of convective Earth models and constraints on radiogenic heat production in the Earth, J. Geophys. Res., 85, 2517–2530, 1980.
Article
Google Scholar
Davies, G. F., Cooling the core and mantle by plume and plate flows, Geophys. J. Int., 115, 132–146, 1993.
Article
Google Scholar
Honda, S., 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, 1995.
Article
Google Scholar
Honda, S., Local Rayleigh and Nusselt numbers for cartesian convection with temperature-dependent viscosity, Geophys. Res. Lett., 23, 2445–2448, 1996.
Article
Google Scholar
Honda, S. and Y. Iwase, Comparison of the dynamical and parameterized models of mantle convection including core-cooling, Earth Planet. Sci. Lett., 139, 133–146, 1996.
Article
Google Scholar
Honda, S. and D. A. Yuen, Cooling model of mantle convection with phase changes: effects of aspect ratio and initial conditions, J. Phys. Earth, 42, 165–186, 1994.
Article
Google Scholar
Howard, L. N., Convection at high Rayleigh number, in Proc. 11th Int. Cong. Appl. Math., edited by H. Görtler, pp. 1109–1115, Springer-Verlag, New York, 1966.
Google Scholar
Iwase, Y., Three-dimensional infinite Prandtl number convection in a spherical shell with temperature-dependent viscosity, J. Geomag. Geoelectr., 48, 1499–1514, 1996.
Article
Google Scholar
Iwase, Y. and S. Honda, An interpretation of the Nusselt-Rayleigh number relationship for convection in a spherical shell, Geophys. J. Int., 130, 801–804, 1997.
Article
Google Scholar
McKenzie, D. P. and N. O. Weiss, Speculations on the thermal and tectonic history of the earth, Geophys. J. R. Astron Soc., 42, 131–174, 1975.
Article
Google Scholar
Nakakuki, T., Studies of convection in the mantle with the phase and the chemical boundaries by numerical simulations, Ph.D. Thesis, Ocean Research Institute, Univ. Tokyo, 1993.
Google Scholar
Patankar, S. V., Numerical Heat Transfer and Fluid Flow, 197pp., Hemisphere Pub. Corp., New York, 1980.
Google Scholar
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, 25473–25484, 1996.
Article
Google Scholar
Schubert, G., Numerical models of mantle convection, Annu. Rev. Fluid Mech., 24, 359–394, 1992.
Article
Google Scholar
Schubert, G., P. Cassen, and R. E. Young, Subsolidus convective cooling histories of terrestrial planets, Icarus, 38, 192–211, 1979.
Article
Google Scholar
Stacey, F. D., Cooling of the earth—A constraint on paleotectonic hypotheses, in Evolution of the Earth, edited by R. J. O’Connell and W. S. Fyfe, Geodyn. Ser., vol. 5, pp. 272–276, AGU, Washington, 1981.
Chapter
Google Scholar
Steinbach, V., D. A. Yuen, and W. Zhao, Instabilities from phase transitions and the timescales of mantle convection, Geophys. Res. Lett., 20, 1119–1122, 1993.
Article
Google Scholar
Stevenson, D. J., T. Spohn, and G. Schubert, Magnetism and thermal evolution of the terrestrial planets, Icarus, 54, 466–489, 1983.
Article
Google Scholar
Tackley, P. J., Effects of strongly temperature-dependent viscosity on time-dependent, three-dimensional models of mantle convection, Geophys. Res. Lett., 20, 2187–2190, 1993.
Article
Google Scholar
Turcotte, D. L. and G. Schubert, Geodynamics, 450pp., John Wiley, New York, 1982.
Google Scholar
van den Berg, A. P. and D. A. Yuen, Convectively induced transition in mantle rheological behavior, Geophys. Res. Lett., 22, 1549–1552, 1995.
Article
Google Scholar
Yuen, D. A., S. Balachandar, V. C. Steinbach, S. Honda, D. M. Reuteler, J. J. Smedsmo, and G. S. Lauer, Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events, Nonlinear Process. Geophys., 2, 206–221, 1995.
Article
Google Scholar