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Influence of lattice thermal conductivity on thermal convection with strongly temperature-dependent viscosity

Abstract

To examine the effects of temperature-dependent lattice thermal conductivity (lattice-k) on the thermal convection with a temperature-dependent viscous fluid, particularly on the upper thermal boundary layer, we have studied numerically 2-D thermal convective flows with both constant thermal conductivity (constant-k) and lattice-k models. Numerical experiments with large viscosity contrasts, greater than a million, produce a cooler and thinner upper thermal boundary layer for the lattice-k compared with those for the constant-k, implying that thermal convection with lattice-k produces a much sharper boundary between the lithosphere and asthenosphere. The differences between the constant-k and lattice-k can be reasonably explained by the following two causes: (i) the decreasing lattice-k with depth increases an effective Rayleigh number around the bottom of the thermal boundary layer, and (ii) the distribution of lattice-k and uniform vertical heat flux within the thermal boundary layer determine the temperature distribution. The predicted sharper boundary, i.e. sharper vertical viscosity gradient near the bottom of the lithosphere, may play an important role on controlling the amount of lithospheric deformation associated with the downwelling.

References

  • Arakawa, A., Computational design for long-term numerical integrations of the equations of atmospheric motion, Comput. Phys., 1, 119–143, 1966.

    Article  Google Scholar 

  • Christensen, U. R., Heat transport by variable viscosity convection and implications for the Earth’s thermal evolution, Phys. Earth Planet. Int., 35, 264–282, 1984.

    Article  Google Scholar 

  • Clark, S. P., Radiative transfer in the Earth’s mantle, Trans. AGU, 38, 931–938, 1957.

    Article  Google Scholar 

  • Deschamps, F. and C. Sotin, Thermal convection in the outer shell of large icy satellites, J. Geophys. Res., 106, 5107–5121, 2001.

    Article  Google Scholar 

  • Dubuffet, F. and D. A. Yuen, A thick pipe-like heat-transfer mechanism in the mantle: nonlinear coupling between 3-D convection and variable thermal conductivity, Geophys. Res. Lett., 27, 17–20, 2000a.

    Article  Google Scholar 

  • Dubuffet, F., D. A. Yuen, and M. Rabinowicz, Effects of a realistic mantle thermal conductivity on the patterns of 3D convection, Earth Planet. Sci. Lett., 171, 401–409, 1999.

    Article  Google Scholar 

  • Dubuffet, F., D. A. Yuen, and T. K. B. Yanagawa, Feedback effects of variable thermal conductivity on the cold downwellings in high Rayleigh number convection, Geophys. Res. Lett., 27, 2981–2984, 2000b.

    Article  Google Scholar 

  • Dubuffet, F., D. A. Yuen, and E. S. G. Rainey, Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity, Nonlinear Process. Geophys., 129, 359–375, 2002.

    Google Scholar 

  • Echelmeyer, K. and B. Kamb, Rheology of ice II and ice III from highpressure extrusion, Geophys. Res. Lett., 13, 693–696, 1986.

    Article  Google Scholar 

  • Frank-Kamenetskii, D. A., Diffusion and Heat Transfer in Chemical Kinetics, Plenum, New York, 1969.

    Google Scholar 

  • Fujisawa, H., N. Fujii, H. Mizutani, H. Kanamori, and S. Akimoto, Thermal diffusivity of Mg2SiO4, Fe2SiO4 and NaCl at high pressures and temperature, J. Geophys. Res., 73, 4727–4733, 1968.

    Article  Google Scholar 

  • Hansen, V. L., J. J. Willis, and W. B. Banerdt, Tectonic overview and synthesis, in Venus II, The University of Arizona Press, Arizona, 1997.

    Google Scholar 

  • Hobbs, P.V., Ice Physics, Clarendon Press, Oxford, England, 1974.

    Google Scholar 

  • Hofmeister, A., Mantle values of thermal conductivity and the geotherm from phonon lifetimes, Science, 283, 1699–1706, 1999.

    Article  Google Scholar 

  • Hofmeister, A., Thermal conductivity of spinels and olivines from vibrational spectroscopy: Ambient conditions, American Mineralogist, 86, 1188–1208, 2001.

    Article  Google Scholar 

  • Hooke, R. Leb., Principles of Glacier Mechanics, Prentice Hall, 1998.

    Google Scholar 

  • Kameyama, M. and M. Ogawa, Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box, Earth Planet. Sci. Lett., 180, 355–367, 2000.

    Article  Google Scholar 

  • Kanamori, H., N. Fujii, and H. Mizutani, Thermal diffusivity measurement of rock-forming minerals from 300 to 1100 K, J. Geophys. Res., 73, 595–605, 1968.

    Article  Google Scholar 

  • Kaula, W. M., Mantle convection and crustal evolution on Venus, Geophys. Res. Lett., 17, 1401–1403, 1990.

    Article  Google Scholar 

  • Kidder, J. G. and R. J. Phillips, Convection-driven subsolidus crustal thickening on Venus, J. Geophys. Res., 101, 23181–23194, 1996.

    Article  Google Scholar 

  • McKinnon, W. B., Sighting the seas of Europa, Nature, 386, 765–767, 1997.

    Article  Google Scholar 

  • McKinnon, W. B., Convective instability in Europa’s floating ice shell, Geophys. Res. Lett., 26, 951–954, 1999.

    Article  Google Scholar 

  • Moresi, L. N. and V. S. Solomatov, Numerical investigation of 2D convection with extremely large viscosity variations, Phys. Fluid., 7, 2154–2162, 1995.

    Article  Google Scholar 

  • Ratcliff, J. T., P. J. Tackley, G. Schubert, and A. Zebib, Transitions in thermal convection with strongly variable viscosity, Phys. Earth Planet. Int., 102, 201–212, 1997.

    Article  Google Scholar 

  • Regenauer-Lieb, K. and D. A. Yuen, Rapid convection of elastic energy into plastic shear heating during incipient necking of the lithosphere, Geophys. Res. Lett., 25, 2737–2740, 1998.

    Article  Google Scholar 

  • Schatz, J. F. and G. Simmons, Thermal conductivity of Earth materials at high temperatures, J. Geophys. Res., 77, 6966–6983, 1972.

    Article  Google Scholar 

  • Schenk, P. M., W. B. McKinnon, D. Gwynn, and J. M. Moore, Flooding of Ganymede’s bright terrains by low-viscosity water-ice lavas, Nature, 410, 57–60, 2001.

    Article  Google Scholar 

  • Schubert, G., D. L. Turcotte, and P. Olson, Mantle Convection in the Earth and Planets, Cambridge University Press, Cambridge, 2001.

    Book  Google Scholar 

  • Solomatov, V. S., Scaling of temperature- and stress-dependent viscosity convection, Phys. Fluids., 7, 266–274, 1995.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tackley, P. J., Effects of strongly temperature-dependent viscosity on timedependent, 3-dimensional models of mantle convection, Geophys. Res. Lett., 20, 2187–2190, 1993.

    Article  Google Scholar 

  • Tatebe, O., The Multigrid Preconditioned Conjugate Gradient Method, Proceedings of Sixth Copper Mountain Conference on Multigrid Methods, NASA Conference Publication, 3224, 621–634, 1993.

    Google Scholar 

  • van den Berg, A. P., D. A. Yuen, and V. Steinbach, The effects of variable thermal conductivity on mantle heat transfer, Geophys. Res. Lett., 28, 575–578, 2001.

    Article  Google Scholar 

  • van den Berg, A. P., D. A. Yuen, and J. R. Allwardt, Nonlinear effects from variable thermal conductivity and mantle internal heating: Implications for massive melting and secular cooling of mantle, Phys. Earth Planet. Inter., 129, 359–375, 2002a.

    Article  Google Scholar 

  • van den Berg, A. P. and D. A. Yuen, Delayed cooling of the Earth’s mantle due to variable thermal conductivity and the formation of a low conductivity zone, Earth Planet. Sci. Lett., 199, 403–413, 2002b.

    Article  Google Scholar 

  • Weinstein, S. A. and U. Christensen, Convection planforms in a fluid with a temperature-dependent viscosity beneath a stress-free upper boundary, Geophys. Res. Lett., 18, 2035–2038, 1991.

    Article  Google Scholar 

  • Weinstein, S. A., P. L. Olson, and D. A. Yuen, Time-dependent large aspect-ratio thermal convection in the Earth’s mantle, Geophys. Astrophys. Fluid Dyn., 47, 157–197, 1989.

    Article  Google Scholar 

  • Yanagawa, T. K. B., M. Nakada, and D. A. Yuen, A simplified mantle convection model for thermal conductivity stratification, Phys. Earth Planet. Int., 146, 163–177, 2004.

    Article  Google Scholar 

  • Zuber, M. T., The crust and mantle of Mars, Nature, 412, 220–227, 2001.

    Article  Google Scholar 

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Correspondence to Tomohiko K. B. Yanagawa.

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Yanagawa, T.K.B., Nakada, M. & Yuen, D.A. Influence of lattice thermal conductivity on thermal convection with strongly temperature-dependent viscosity. Earth Planet Sp 57, 15–28 (2005). https://doi.org/10.1186/BF03351802

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  • DOI: https://doi.org/10.1186/BF03351802

Key words

  • Mantle convection
  • lattice thermal conductivity
  • variable viscosity