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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 2, issue 3/4
Nonlin. Processes Geophys., 2, 206–221, 1995
https://doi.org/10.5194/npg-2-206-1995
© Author(s) 1995. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Complex space-time geophysical structures

Nonlin. Processes Geophys., 2, 206–221, 1995
https://doi.org/10.5194/npg-2-206-1995
© Author(s) 1995. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Dec 1995

31 Dec 1995

Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events

D. A. Yuen1, S. Balachandar2, V. C. Steinbach3, S. Honda4, D. M. Reuteler2, J. J. Smedsmo1, and G. S. Lauer1 D. A. Yuen et al.
  • 1Dept. Geology, Geophysics and Minnesota Supercomputer Inst., Univ. of Minnesota, Minneapolis, MN 55415-1227, USA
  • 2Dept. of Theretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
  • 3Inst. für Geophysik und Meteorologie, Universität zu Köln, 60923 Köln, Germany
  • 4Dept. of Earth and Planetary Systems Science, Faculty of Science, University of Hiroshima, Higashi-Hiroshima 739, Japan

Abstract. We have examined the non-equilibrium effects of core-cooling and time-dependent internal-heating on the thermal evolution of the Earth's mantle and on mantle flush events caused by the two major phase transitions. Both two- and three-dimensional models have been employed. The mantle viscosity responds to the secular cooling through changes in the averaged temperature field. A viscosity which decreases algebraically with the average temperature has been considered. The time-dependent internal-heating is prescribed to decrease exponentially with a single decay time. We have studied the thermal histories with initial Rayleigh numbers between 2 x 107 and 108 . Flush events, driven by the non-equilibrium forcings, are much more dramatic than those produced by the equilibrium boundary conditions and constant internal heating. Multiple flush events are found under non-equilibrium conditions in which there is very little internal heating or very fast decay rates of internal-heating. Otherwise, the flush events take place in a relatively continuous fashion. Prior to massive flush events small-scale percolative structures appear in the 3D temperature fields. Time-dependent signatures, such as the surface heat flux, also exhibits high frequency oscillatory patterns prior to massive flush events. These two observations suggest that the flush event may be a self-organized critical phenomenon. The Nusselt number as a function of the time-varying Ra does not follow the Nusselt vs. Rayleigh number power-law relationship based on equilibrium (constant temperature) boundary conditions. Instead Nu(t) may vary non-monotonically with time because of the mantle flush events. Convective processes in the mantle operate quite differently under non-equilibrium conditions from its behaviour under the usual equilibrium situations.

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