Physics
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000pepi..119..321c&link_type=abstract
Physics of the Earth and Planetary Interiors, Volume 119, Issue 3-4, p. 321-336.
Physics
30
Scientific paper
The present numerical study describes the transient cooling process of a variable viscosity fluid in the conductive lid regime. The quasi-static hypothesis, assuming that each time-step can be considered as a steady-state heat transfer, is further investigated. A first period of the cooling is essentially transient. Two stages are observed: (1) onset time for convection and (2) convective adjustment period. Onset of convection is seriously delayed when compared to isoviscous thermal convection. The numerical experiments are well described by a boundary layer analysis that we propose, predicting that the dimensionless convective onset time τo can be scaled as a function of a viscous temperature scale ΔTv linked to the rheological characteristics of the thermal boundary layer [Davaille, A., Jaupart, C., 1993. Transient high-Rayleigh-number thermal convection with large viscosity variations. J. Fluid Mech., 253, 141-166.], the internal Rayleigh number Rai and the temperature drop ΔT across the fluid layer:τo~Rai-2/38/3Due to the slow diffusive heat transfer of the first thermal instabilities through the conductive lid, a convective adjustment stage follows the onset of convection. It is shown that this duration ΔτII is linked to the square of the conductive lid thickness δ:ΔτII~δ2Application to the thermal evolution of planetary interiors indicates that this initial transient period is shorter than a few hundreds of million years. The subsequent cooling in the conductive lid regime is shown to be quasi-static. The conductive lid, however, is not equivalent to the elastic lithosphere, as thermal history models usually assume. Cooling numerical experiments described in the present paper are in good agreement with the scaling law describing steady-state heat transfer below a conductive lid.
Choblet Gaël
Sotin Ch.
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