Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 2 3/4 1995 10.5194/npg-2-206-1995 http://www.nonlin-processes-geophys.net/2/206/1995/ http://www.nonlin-processes-geophys.net/2/206/1995/npg-2-206-1995.html http://www.nonlin-processes-geophys.net/2/206/1995/npg-2-206-1995.pdf 206 221 0000-00-00 Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events D. A. Yuen S. Balachandar V. C. Steinbach S. Honda D. M. Reuteler J. J. Smedsmo G. S. Lauer Dept. Geology, Geophysics and Minnesota Supercomputer Inst., Univ. of Minnesota, Minneapolis, MN 55415-1227, USA Dept. of Theretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA Inst. für Geophysik und Meteorologie, Universität zu Köln, 60923 Köln, Germany Dept. of Earth and Planetary Systems Science, Faculty of Science, University of Hiroshima, Higashi-Hiroshima 739, Japan 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 <i>Nu(t) </i> 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.