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

David A Yuen, S. Balachandar, V. C. Steinbach, S. Honda, D. M. Reuteler, J. J. Smedsmo, G. S. Lauer

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16 Scopus citations

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 × 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 3-D 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 behavior under the usual equilibrium situations.

Original languageEnglish (US)
Pages (from-to)206-221
Number of pages16
JournalNonlinear Processes in Geophysics
Volume2
Issue number3-4
DOIs
StatePublished - 1995

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