Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles

The parallelized three-dimensional spherical convection code, TERRA, is employed to study the mean temperatures and planforms of convecting planetary mantles in spherical shell geometries. We vary the factor f which controls the degree of Curvature, defined as the ratio of the radii of the inner and outer bounding surfaces, the Benard-Rayleigh number, Rag. and the dimensionless rate of internal heating, H. We develop parameterized expressions for predicting the mean temperature of connecting spherical shells which are heated partially from within and partially from below by a hot isothermal lower boundary. Our parameterization is fit to a data set of mean temperatures from 23 numerical model calculations for f = 0.547 (appropriate to Earth's mantle). We then demonstrate that this parameterization of mean temperature in terms off, Rag and H extends to other values off as well. For all values off, ROB and H considered in this study, our predicted mean temperatures agree with the model calculations to within 2.4%. The scaling analysis is extended to obtain an expression for surface heat flux in terms of ROB and H for f = 0.547. In that case we obtain a predictive equation for surface heat flux that agrees to within 11% of the observed values. Our findings provide a useful tool for parameterizing the temperature and surface heat flux of planetary mantles of varying geometry and heating configurations.

@article{id1375,
  author = {Shahnas, M. Hosein and Lowman, Julian P. and Jarvis, Gary T. and Bunge, Hans-Peter},
  doi = {10.1016/j.pepi.2008.04.007},
  journal = {PHYSICS OF THE EARTH AND PLANETARY INTERIORS},
  language = {en},
  number = {1-2},
  pages = {6-15},
  title = {Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles},
  volume = {168},
  year = {2008},
}

%O Journal Article
%A Shahnas, M. Hosein
%A Lowman, Julian P.
%A Jarvis, Gary T.
%A Bunge, Hans-Peter
%R 10.1016/j.pepi.2008.04.007
%J PHYSICS OF THE EARTH AND PLANETARY INTERIORS
%G en
%N 1-2
%P 6-15
%T Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles
%V 168
%D 2008