Onset of convection in a basally heated spherical shell application to planets

Details Onset of convection in a basally heated spherical shell application to planets Onset of convection in a basally heated spherical shell application to planets

Dec 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufm.v13b2124b&link_type=abstract

American Geophysical Union, Fall Meeting 2008, abstract #V13B-2124

Physics

0545 Modeling (4255), 5455 Origin And Evolution

Scientific paper

Convective instabilities related to the early dynamics of planetary mantles just after core formation play an important role in the subsequent evolution. Although these early stages of planetary dynamics are likely to imply more complex phenomena such as global melting and fractional solidification, little is known about the onset of solid-state convection in a fluid with temperature-dependent viscosity heated from below. Here, we investigate onset times of convection in a spherical shell in order to obtain scaling laws with Rayleigh number, viscosity parameter describing the dependency on the temperature and geometry of the shell. The influence of the mechanical boundary condition is also studied: free-slip is relevant for planetary mantles overlying a fluid core while no-slip may better approximate the boundary condition between two solid layers (e.g. between an icy layer and a silicate core in some of the icy satellites). We performed three dimensional numerical experiments in a spherical shell using the OEDIPUS program (Choblet, 2005; Choblet et al., 2007). The fluid is incompressible, its viscosity is temperature dependent and the Boussinesq approximation is used. We systematically investigate the onset time and wavelength of the first instabilities. Furthermore, in order to better understand the processes associated to the birth of convection, 3D results are compared to onset times obtained with two simple methods: the linear stability (LS) analysis and the growth of the Rayleigh- Taylor (R-T) instabilities. For the LS analysis, the values of the onset time are much smaller due to the "frozen time" approach. Moreover, the dependency of the onset time on the Rayleigh number is overestimated, especially for the free-slip conditions, where the effect of the frozen time is even more significant due to kinematic effects. For the R-T instability analysis, however, the onset times are also slightly underestimated, the agreement with 3D numerical simulations is good in terms of efficient scaling relationships. For both free-slip and no-slip boundary condition, the scaling may be written in the form t~(Ra*)a, where a is approximately -2/3 and Ra*=Ra(μ(θ*)) is A Rayleigh number specifically associated to a relevant viscosity (temperature) value. Planetary implications are envisioned.

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