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

A.P. van den Berg et al. / Physics of the Earth and Planetary Interiors 149 (2005) 259–278 271
Fig. 12. Global 1D depth profiles of horizontally averaged temperature (left), conductivity (middle) and viscosity (right). Results are for the
same initial CMB temperature of T CMB (0) = 3773 K and for an integration time t = 2.952 Gyr.
boundary layer thinner at the top and thicker at the bottom,
compared to the constant conductivity case. This
can be interpreted in terms of the different systematics
of the thermal resistance profiles defined in (6), through
the top and bottom boundary layers, as discussed in
more detail below. Increased thermal resistance of the
top boundary layer has in increasing effect on the temperature
contrast across the lithosphere. Similarly the
decreased resistance near CMB results in a decreased
temperature contrast across CMB.
We see that the viscosity profiles are all very similar
but that the conductivity and temperature profiles reveal
sharp changes with the amount of enhanced radiative
conductivity from subadiabatic to superadiabatic
gradient. Thus one cannot casually employ a constant
value thermal gradient in the lower mantle for determining
the viscosity profile (Yamazaki and Karato,
2001). There is a dramatic variation in the shape of
〈k〉 for values of f exceeding 3. This ‘transition’ is also
reflected in the character of the temperature gradient in
the bottom part of the mantle. The temperature gradient
for f = 5 shows a superadiabatic character, in contrast
to the models with lower f values, which show a subadiabatic
geotherm in the bottom parts of the mantle.
We obtained similar results in models with a zero heat
flux bottom boundary condition (van den Berg et al.,
2002). The super adiabatic geotherm is consistent with
the mineral physics result of da Silva et al. (2000) on
the basis of the bulk modulus variation with depth. This
superadiabatic character of the geotherm may indicate
an enhanced radiative heat transfer in the deep mantle.
This high temperature gradient in the lower mantle, due
to enhanced radiative heat transfer, is also reminiscent
of temperature distributions resulting from an abyssal
source of radiogenic heating invoked in the deep mantle
model by Kellogg et al. (1999).
The evolution of the thermal-mechanical structure
near the CMB is shown in Fig. 13, where we plot
the 〈T 〉, 〈η〉 and 〈k〉 profiles for constant conductivity,
f = 0, 1 and 5. The effect of variable thermal conductivity
is to retard the growth of the thermal boundary
layer. With larger values of f the growth rate of the
boundary layer approaches that associated with a constant
thermal conductivity.
We see that the more efficient heat transfer in the
case of f = 5 gives rise to a cooler lower mantle temperature
and hence a shallower trough in the viscosity
at the CMB.
The time evolution of the temperature contrast
δT across the thermal boundary layer at the CMB
is shown in Fig. 14. These temperature contrasts
where calculated as the difference, δT (t) = T CMB (t) −
T A (z CMB , t), between the actual CMB temperature and
the extrapolated CMB temperature T A (z CMB , t) of a
mantle adiabat obtained by a least squares estimate,
for the depth range between 1000 and 1800 km depth,