Physics
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.v44b..09d&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #V44B-09
Physics
[5455] Planetary Sciences: Solid Surface Planets / Origin And Evolution, [8121] Tectonophysics / Dynamics: Convection Currents, And Mantle Plumes, [8125] Tectonophysics / Evolution Of The Earth, [8130] Tectonophysics / Heat Generation And Transport
Scientific paper
Most terrestrial planets may have experienced a magma ocean period in their infancy where most of their mantle was molten. Upon cooling to space, their surface must have crystallized, keeping a largely molten interior for some more time. The dynamics and evolution of planets at this stage is controlled by the surface heat flow, which is dominated by volcanism. This is in sharp contrast with the current situation on these planets (with the notable exception of Io) where heat is carried through the top surface of the mantle by diffusion. We developed a new set of semi permeable boundary conditions in order to take into account heat advection and diffusion through the top surface. We incorporated them in 2- and 3-D cartesian models of infinite Prandtl number thermal convection in the Boussinesq approximation. We imposed a no shear stress boundary condition on the top surface. In contrast to standard mantle convection models, the vertical velocity is not set to zero but generates a topography that obeys a diffusion equation in order to model processes such as magma spreading or erosion. We impose a zero temperature for down-welling currents, and a zero vertical temperature gradients for upwelling currents. Melting and freezing processes are modeled using a viscosity that varies sharply by a few orders of magnitude at the melting temperature and by using an enthalpy equation to take account of latent heat effects. We have run experiments with either internal heating or bottom heating. The variation of the diffusivity coefficient for the topography allows the models to go continuously from thermal convection with permeable surface boundary to thermal convection with impermeable one. The pattern of convection and heat transfer characteristics are strongly affected by the choice of boundary conditions. We obviously find a more efficient heat transfer with permeable boundary conditions than with impermeable ones. The scaling laws we get can be used to compute the thermal evolution of young planets at the end of the magma ocean stage and the results compare well with full dynamical calculation with evolving conditions. Temperature maps for three cases with Ra=106 with different boundary conditions
Dubuffet Fabien
Labrosse Stephane
Ricard Y. R.
Ulvrova M.
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