van den Berg et al., 2005, Earth Planetary Science Letters.

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272 A.P. van den Berg et al. / Physics of the Earth and Planetary Interiors 149 (2005) 259–278 Fig. 13. Profiles of horizontally averaged temperature (left column), conductivity (middle column) and viscosity (righthand column) for the bottom 300 km of the mantle. Models shown are for an initial CMB temperature T CMB (0) = 3773 K. Different curves in each panel correspond to different integration times, t = 0, 2.36 and 5.02 Gyr, and the direction of increasing time is indicated by the arrows. The columns shown correspond to different conductivity models, constant k (top), f = 1, 0 and 5.
A.P. van den Berg et al. / Physics of the Earth and Planetary Interiors 149 (2005) 259–278 273 Fig. 14. Evolution in time of the temperature contrast across the thermal boundary layer at the CMB. Different initial CMB temperature are shown T CMB (0) = 3273, 3773, 4273. Each panel shows results for different conductivity models, constant k, f = 0, 1 and 5. based on the horizontally averaged 1D temperature profile. The constant k models show the highest temperature contrast, as are also illustrated in the temperature profiles of Fig. 12. The temperature contrast for the variable k cases increases with f between f = 0 and 5. A more rapid development of a higher temperature contrast δT may explain a larger tendency towards early plume formation from the CMB in the constant conductivity cases. Considering the effects of the structure of the bottom thermal boundary layer on the cooling of the core, we see that the high δT value for the constant k case is apparently compensated by a lower conductivity value, as shown in Fig. 12(middle), resulting in an intermediate core heat flux, which can be observed clearly in Fig. 9. More insight can be obtained in the trends in the model results for enhanced radiative conductivity by comparing profiles of the 1D thermal resistance defined Fig. 15. Vertical profiles of horizontally averaged conductivity 〈k〉 (left), resistivity 〈1/k〉 (middle) and corresponding thermal resistance R(z) (right). Blue and green curves correspond to snapshots, evenly spaced in time from 0 to 4.55 Gyr, for two models with contrasting contribution of the radiative conductivity, k rad = 0, f = 0 (green), amplified k rad , f = 10 (blue). The top row of frames shows a zoom in on the top 500 km of the model. The bottom row shows the bottom boundary layer.
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van den Berg et al., 2005, Earth Planetary Science Letters.

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