Mathematics – Logic
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufmmr11a..08v&link_type=abstract
American Geophysical Union, Fall Meeting 2005, abstract #MR11A-08
Mathematics
Logic
5418 Heat Flow, 5430 Interiors (8147), 8130 Heat Generation And Transport
Scientific paper
Over the past several decades, scaling laws relating the heat flow, expressed as the Nusselt number, of a convecting system (in casu a planetary mantle) to its convective vigour, expressed in the form of a thermal Rayleigh number, have greatly helped us to understand the thermal evolution of our planet and its sisters. Recently, however, it has become increasingly clear that compositional buoyancy may play an important role in several small and large scale geodynamic processes, including the subduction (or not) of oceanic lithosphere and the stability of continents. As these processes play a significant role in the removal of heat from the planetary interior, it is important to take these effects into account when considering the planetary thermal evolution. In this work we present the results of an effort to study and parameterize the effects of partial melting induced chemical differentiation (affecting density) and dehydration (af fecting viscosity) on the classical scaling laws for heat flow and their more recent derivatives. From a total of 155 self-consistently differentiated numerical experiments for varying rheological parameters and melting conditions, around 180 periods considered to be in or very near to a statistical steady state were selected and characterized in terms of parameters relevant to heat flow and convective vigour. The resulting information was used to investigate the sensitivity of the heat flow scaling laws to the differentiation. Three different differentiated regimes were observed: 1) Full chemical lid; 2) partial chemical lid; 3) advection of depleted material. These occur for varying thermal conditions and rheological parameters (i.e. sensitivity of the viscosity to temperature and water content). Scaling laws for the heat flow as a function of convective vigour show values for the exponent β that depend on the regime and that may be significantly smaller than for purely thermal convection cases.
Lognonné Philippe
van Thienen P.
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