HR: 0830h
AN: T11C-0407    [PDF]
TI: Impact of Temperature and Pressure Dependent Thermal Conductivity and Viscosity and Core-Mantle Coupling on Planetary Thermal Evolution
AU: * van den Berg, A P
EM: berg@geo.uu.nl
AF: Dept. Theoretical Geophysics, Utrecht University, Inst. Earth Science, Budapestlaan 4, Utrecht, 3508 TA Netherlands
AU: Rainey, E S
EM: emma@gps.caltech.edu
AF: Planetary sciences division, Caltech, MC-150-21, Pasadena, CA 91125 United States
AU: Yuen, D A
EM: davey@msi.umn.edu
AF: Dept. Geology and Geophysics and University of Minnesota Supercomputer Institute, University of Minnesota, 108 Pillsbury Hall 310 Pillsbury Dr SE, Minneapolis, MN 55455-0219 United States
AB: Secular cooling of terrestrial planets is largely controled by the heat transport through thermal convection of the silicate mantle enclosing the metallic core. Similar to the well known temperature dependence of mantle viscosity $\eta (T)$ (Tozer, 1972), thermal conductivity $k$, dominated by a lattice dynamical component $k_{lat}$ as in Hofmeisters (1999) model, also decreases with temperature. In previous work we have shown, for isoviscous models, without mantle core coupling, that secular cooling is substantially delayed, by one to two billion year, for models based on variable $k(T,P)$, compared to constant $k$ models. Here we present results of numerical mantle convection models for both variable $k(T,P)$ and $\eta (T,P)$ and we also consider thermal coupling between the mantle and the core, represented by an isothermal heat reservoir. The results show that the delay in secular cooling of the models with variable conductivity of the Hofmeister type, compared to the constant $k$ model, is a robust feature also in mantle convections models with variable viscosity. These results show that thermal conductivity, like viscosity, playes a major role in controling planetary thermal evolution. The thermal evolution of the core is driven by conductive heat transport through the core mantle boundary (CMB) and is therefore also sensitive to the particular model of thermal conductivity. In this respect the radiative conductivity component $k_{rad}$, related to phonon transport is particularly important as it increases with temperature and plays a stabilizing role in the bottom thermal boundary layer. Our results show that the temperature contrast $\delta T$ across the thermal boundary layer at the bottom of the mantle continues to increase from a zero initial value to values between $400 K$ and $800 K$, for variable $k$ and constant $k$ respectively and within the variable $k$ models $\delta$ increases with the relative contribution of the radiative conductivity $k_{rad}$. The smaller temperature contrast across the bottom thermal boundary layer for the variable $k$ models is reflected in a reduced tendency for plume formation at the CMB in the variable $k$ models. The heatflux from the core shows an increasing tendency with time and strong fluctuations originating from thermal interaction of the core with cold downwellings and hot upwellings in the mantle convective flow at the CMB. We varied the initial CMB temperature between $3273$ and $4273 K$ and found that high $T_{CMB}$ results in higher cooling rates, stronger time dependence and an increased contribution of the radiatiative conductivity $k_{rad}$. In general we found the cooling rate of the mantle to be strongly time dependent, fluctuating around values of $100 - 150 K/Gyr$. These mean values are fairly constant or even slightly increasing with time, illustrating the buffering effect of the core heat flux, increasing with time.
DE: 3210 Modeling
DE: 5134 Thermal properties
DE: 5418 Heat flow
DE: 8121 Dynamics, convection currents and mantle plumes
DE: 8125 Evolution of the Earth
SC: Tectonophysics [T]
MN: 2003 Fall Meeting