Numerical experiments on thermal convection in a chemically stratified viscous fluid heated from below: implications for a model of lunar evolution

Details Numerical experiments on thermal convection in a chemically stratified viscous fluid heated from below: implications for a model of lunar evolution Numerical experiments on thermal convection in a chemically stratified viscous fluid heated from below: implications for a model of lunar evolution

May 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998pepi..108...15p&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 108, Issue 1, p. 15-32.

Physics

12

Scientific paper

Compositional density differences resulting from the initial differentiation or secular evolution of planetary mantles can create buoyancy forces comparable to, or even larger than, those caused by thermal expansion. This study examines two and three-dimensional numerical experiments on thermal convection in a stably stratified, infinite Prandtl number fluid heated from below at a prescribed rate. A thermally and chemically well-mixed convecting layer forms and thickens with time. The layer thickness and temperature as functions of time are determined for a range of thermal and compositional Rayleigh numbers. In some cases a second layer forms above the first, and we examine a criterion for its formation based on the critical Rayleigh number of the conductive thermal boundary layer above the first convecting layer. When a second layer is not present, the thickness of the convecting, well-mixed layer increases approximately as the square-root of time at a rate that depends on the ratio of compositional and thermal buoyancy but which is independent of the thermal Rayleigh number. We show that this thickening rate and the temperature in the mixed layer are well described by a simple physical parameterization that assumes a thermally and compositionally uniform mixed layer and a density at the top of the mixed layer that is the same as that in the immediately overlying, still stably stratified fluid. These results may have a variety of implications for planetary evolution. Here we focus on a model for the evolution of the Moon in which gravitational differentiation of the unstable stratification resulting from solidification of a magma ocean creates a stably stratified mantle with dense, late stage, ilmenite-cumulates forming a U- and Th-rich core which heats the overlying mantle. Compositional stratification in the mantle traps heat in the interior and prevents the rapid formation of plumes capable of generating surface volcanism. Melting at the top of a gradually thickening heated mixed layer in the mantle can explain the age of onset and the depth of origin of the high and low-Ti mare basalts. This may also explain the thick elastic lithosphere and mascon gravity anomalies that developed at the time of mare volcanism. The results of our numerical experiments allow a more rigorous examination of this model of lunar evolution.

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