The effects of a variation of the radial viscosity profile on mantle evolution

The present paper describes a set of numerical experiments on the mantle's thermal evolution with an infinite Prandtl number fluid in a compressible spherical shell heated mainly from within. We used the anelastic liquid approximation with Earth-like material parameters. The usual variable-viscosity approach in mantle-convection models is the assumption of a temperature dependence only. The resulting thermal boundary layers are included in our model also, but an additional viscosity profile of the interior mantle was derived: The Birch–Murnaghan equation was employed to derive the Grüneisen parameter and other physical quantities as a function of depth from observational values provided by PREM. We computed the melting temperature and a new mantle viscosity profile, called eta3, using the Grüneisen parameter, Lindemann's law and some solid-state physics considerations. The new features of eta3 are a high-viscosity transition layer with rather high viscosity gradients at its boundaries, a second low-viscosity layer beginning under the 660-km discontinuity, and a strong viscosity increase in the central parts of the lower mantle. The rheology is Newtonian but it is supplemented by a viscoplastic yield stress, σ_y. A viscosity-level parameter, r_n, and σ_y have been varied. For a medium-sized Rayleigh-number–yield-stress area, eta3 generates a stable, plate-tectonic behavior near the surface and simultaneously thin sheet-like downwellings in the depth. Outside this area, three other types of solution were found. Not only the planforms but also the evolution of the Rayleigh number, the reciprocal Urey number, the Nusselt number, the surface heat flow, etc., have been studied. We repeated this investigation with two very different basic viscosity profiles, etaKL5a and etaKM, of other authors. A comparison reveals that eta3 facilitates the generation of surface plates and thin sheet-like downwellings in the depth considerably more than etaKL5a or even etaKM. The presence of two internal low-viscosity layers is obviously conducive for plateness and thin sheet-like downwellings. For an infinite yield stress, the thin cold sheet-like downwellings are reticularly connected. However, the distribution of the downwellings is more Earth-like if a realistic yield stress is added.