Secular Cooling Rates of the Mantle : Various Influences

Details Secular Cooling Rates of the Mantle : Various Influences Secular Cooling Rates of the Mantle : Various Influences

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufm.u72b0029r&link_type=abstract

American Geophysical Union, Fall Meeting 2002, abstract #U72B-0029

Physics

3210 Modeling, 8121 Dynamics, Convection Currents And Mantle Plumes, 8125 Evolution Of The Earth, 8130 Heat Generation And Transport

Scientific paper

The history of secular cooling of the mantle is an old important issue, which has been attacked for many years using temperature-dependent viscosity as the primary agent (Tozer, 1972. Phys. Earth Planet. Int., 6, 182-197). In this work we have ventured to look at the impact of variable thermal conductivity on the secular cooling rates predicted by models using just temperature-dependent viscosity. We have found the following salient results. (1) A delayed secular cooling is found as in the constant viscosity models (van den Berg and Yuen, 2002, Earth Planet. Sci. Lett., 199, 403-413, van den Berg et al., 2002, Phys. Earth Planet. Inter., 129, 359-375). We have applied an exponential temperature and pressure dependent viscosity model, using thermal viscosity contrast up to 3000 and fixed presssure viscosity contrast of 100 for this verification. (2) A purely depth-dependent thermal conductivity k(P) cannot catch the destructive effect of temperature dependent conductivity on the negative thermal buoynacy of cold downwellings, driving the convective circulation. These k(P) models also lack feedback physics between time-dependent internal heating and variable thermal conductivity k(T,P), thus stressing the need to use k(T,P) whenever there is a strong source of heat present. (3) Large-differences occur between predictions from 2-D numerical models based on Partial Differential Equations (PDE) and averaged parameterized convection models, formulated using an Ordinary Differential Equation (ODE), within the framework of integrating the nonlinear ODE for the volume average temperature. The ODE results for this comparison are computed using the time series of volume average quantities (viscosity, conductivity) obtained from the 2-D PDE results. The comparison shows that the 1-2 Gyr delay in secular cooling, characteristic for full convection PDE models, is not reproduced in the ODE results from parameterized convection models. The temperature dependence of the ice thermal conductivity may also have a strong impact on thermal evolution of icy satellites in the outer solar system, controlled by conductive and convective heat transport in the outer ice shell (Deschamps and Sotin, 2001. J. Geophys. Res., 106, 5107-5121). Our results indicate there are still remaining some severe issues regarding the usage of parametrized convection in the traditional sense.

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