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 temperautre at the core-mantle boundary. TCMB, 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 TCMB strengthens convective vigor and leads to a non-linear increase of averaged temperature, heat-flow and root-mean-squared velocity. The interior ciscosity decreses strongly with TCMB and internal heating due to radioactivity. A viscosity maximum is found in the horizontally averaged viscosity profile at depth around 2000km. 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 TCMB shows a relatively insensitive increase of Nu with TCMB. In terms of an effective Rayleigh number of the whole system, RaE, the power-law exponent of the Nu(RaE) 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.
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We acknowledge discussions with Shun Karato and Ondřej Čadek about the issue of the superadiabatic geothermal gradient in the lower mantle and insightfull comments by two anonymous reviewers. This research has been supported by NATO and the geophysics program of the National Science Foundation.