Modelling planetary dynamics by using the temperature at the core–mantle boundary as a control variable: effects of rheological layering on mantle heat transport

Abstract

In planetary convection, there has been a great emphasis laid on the usage of the Rayleigh number as a control parameter for describing the vigor of convection. However, realistic mantle rheology not only depends on temperature, pressure, strain-rate and composition, but also on the nature of the dominant creep mechanism, which varies with pressure and also with temperature. It is difficult to study the effects of varying influences from the convective strength without also changing the mantle flow law in the process. We have adopted the approach of using as the sole control parameter, the temperature at the core–mantle boundary, T CMB, in modelling planetary dynamics with a composite non-Newtonian and Newtonian rheology, which is temperature-dependent in the upper mantle and both temperature- and pressure-dependent in the lower mantle. Increasing the T CMB strengthens convective vigor and leads to a non-linear increase of averaged temperature, heat-flow and root-mean-squared velocity. The interior viscosity decreases strongly with T CMB and internal heating due to radioactivity. A viscosity maximum is found in the horizontally averaged viscosity profile at a depth around 2000 km. This viscosity hill moves downward with diminishing amplitude in the face of increasing dissipation number and internal heating. The bottom third of the lower mantle appears to be superadiabatic as a consequence of the stiff lower-mantle rheology. The scaling relationship between the Nusselt (Nu) number and T CMB shows a relatively insensitive increase of Nu with T CMB. In terms of an effective Rayleigh number of the whole system, Ra E, the power-law exponent of the Nu (Ra E) relationship is very low, around 0.12. Strong pressure-dependence of lower-mantle rheology and its large volume relative to the entire mantle would induce a much lower cooling rate of the planet than previous models based on parameterized convection with a temperature-dependent viscosity.