We present a set of 3-D numerical experiments on the mantle’s thermal evolution in a compressible spherical shell with Earth-like material parameters. The model is homogeneously heated from within. ( 238 U, 235 U, 232 Th, 40 K) ; Abundances according to McCulloch & Bennett (1994) Small additional heating from below (CMB)

What is new? [New in comparison with Walzer, U., Hendel, R., Baumgardner, J., Viscosity stratification and a 3-D compressible spherical shell model of mantle evolution. In: Krause, E., Jäger, W., Resch, M. (Eds.), High Performance Computing in Science and Engineering‘03, pp , Springer-Verlag, Berlin, Heidelberg, New York, ISBN ] New model: Walzer, U., Hendel, R., Baumgardner, J., The effects of a variation of the radial viscosity profile on mantle evolution, Tectonophysics 384, Newly derived melting curve of the mantle New viscosity profile with big jumps at the phase boundaries Viscoplastic yield stress  y Another thermal boundary condition at CMB: The CMB is assumed to be laterally isothermal at a particular time. Like other autors (Steinbach et al., 1993; Honda and Yuen, 1994) we adjust T cmb after each time step according to the heat transported from the core to the mantle.

The PREM values have been smoothed for each layer f=2 V.Z.; PREM P, K,  K/  P

 simplification

ALA The term is neglected. We obtain Conservation of mass Conservation of momentum Deviatoric stress tensor Adams-Williamson

This is the conservation of energy, where A less known expression of the conservation of energy is Equation of state

Thermal evolution of a 3-D compressible mantle with pressure- and temperature-dependent viscosity and time-dependent heating from within. Spherical shell Based on v p, v s,  of PREM, an experimental  (P) and solid-state physics, we derived the Grüneisen parameter, , the specific heats, c P and c v, and a new melting temperature, T m (r). A new radial viscosity profile, eta3, of the mantle with steep gradients at the known mineral phase boundaries High-viscosity transition layer, a second low-viscosity layer below the 660, a strong viscosity rise in the central part of the LM eta3 with its two low-viscosity layers plus viscoplastic yield stress facilitates the generation of stable, plate-tectonic behavior. I

Variation of non-dimensional numbers (Ra, Nu, Ur, r n ) Variation of the yield stress,  y, and Ra H (2) reveals four types of solutions. For intermediate values of  y and Ra H (2), we obtain plate-like movements along the surface with plate-like downwelling sheets. Solutions with infinite  y show only plate-like downwelling sheets but no plates near the surface.