Regime classification and planform scaling for internally heated mantle convection

Hüttig, Christian; Breuer, D.

doi:10.1016/j.pepi.2011.03.011

Cited by 13 publications

(11 citation statements)

References 82 publications

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“…In this regime stagnant-lid convection occurs. Ratcliff et al (1997) and Hüttig & Breuer (2011) find a low-degree regime for bottom-heated and purely internally heated convection in a three-dimensional spherical shell, respectively. This regime has been found to lie between the mobile-lid and stagnant-lid domains and is characterized by long wavelengths.…”

Section: B Futterer Et Almentioning

confidence: 99%

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

et al. 2013

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We introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh-Bénard convection that have been performed for both temperatureindependent ('GeoFlow I') and temperature-dependent fluid viscosity properties ('GeoFlow II') with a measured viscosity contrast up to 1.5. To set up a selfgravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the 'GeoFlow' experiments. We use Wollaston prism shearing interferometry for flow visualization -an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In 'GeoFlow I', we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in 'GeoFlow II', we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the 'GeoFlow II' experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.

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Section: B Futterer Et Almentioning

confidence: 99%

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

et al. 2013

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“…We employed the finitevolume code Gaia (e.g., Hüttig & Breuer 2011) to solve the conservation equations of mass, momentum, and thermal energy for a creeping fluid with depth-dependent viscosity in a twodimensional (2-D) cylindrical shell. We introduce three non-dimensional quantities that characterize our convective systems (Table 5): the thermal Rayleigh number Ra, the Rayleigh number for internal heat sources Ra , and the dissipation number Di.…”

Section: Non-dimensional Numbersmentioning

confidence: 99%

Rocky super-Earth interiors

Wagner

Tosi

Sohl

et al. 2012

A&A

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Aims. We present interior structure models of the recently discovered exoplanets CoRoT-7b and Kepler-10b addressing their bulk compositions, present thermal states, and internal dynamics. We investigate how mantle convection patterns are influenced by the depth-dependence of thermodynamic parameters (e.g., thermal expansivity and conductivity) caused by the extended pressure and temperature ranges within rocky super-Earths. Methods. To model the interior of rocky exoplanets, we construct a four-layer structural model solving the mass and energy balance equations in conjunction with a generalized Rydberg equation of state providing the radial density distribution within each layer. The present thermal state is calculated according to a modified mixing-length approach for highly viscous fluids. Furthermore, the obtained internal structure is used to carry out two-dimensional convection simulations to visualize the mantle convection pattern within massive exoplanets such as CoRoT-7b and Kepler-10b. Results. Both CoRoT-7b and Kepler-10b most likely have large iron cores and a bulk composition similar to that of Mercury. For a planetary radius of R p = (1.58 ± 0.10) R ⊕ , a revised total mass of M p = (7.42 ± 1.21) M ⊕ , and the existence of a third planet in the CoRoT-7 planetary system, calculations suggest that an iron core of 64 wt-% and a silicate mantle of 36 wt-% is produced owing to the relatively high average compressed density of ρ avg = (10.4±1.8) g cm −3 . Kepler-10b's planetary radius and total mass yield an iron core of 59.5 wt-%, which complements the silicate mantle of 40.5 wt-%. An enhanced radiogenic heating rate owing to CoRoT-7b's young age (1.2−2.3 Gyr) raises the radial distribution of temperature by only a few hundred Kelvin, but reduces the viscosity by an order of magnitude. The planform of mantle convection is found to be strongly modified for depth-dependent material properties, with hot plumes rising across the whole mantle and cold slabs, which stagnate in the mid-mantle because of the loss of buoyancy. Conclusions. We use a new model approach to determine the detailed interior structures and present thermal states of CoRoT-7b and Kepler-10b. Both planets are found to be enriched in iron. The results imply that modest radiogenic heating does not play a significant role in determining the internal structure of rocky exoplanets. The depth-dependence of thermodynamic properties, however, strongly influences the mantle convection patterns within exoplanets such as . This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

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“…Depending on the viscosity contrast, convection may reach to the top (and cold) surface or a stagnant lid may form underneath that surface. Four different regimes have been identified (e.g., Hansen and Yuen 1993;Solomatov 1995;Trompert and Hansen 1998;Huettig 2009) (Fig. 1):…”

Section: Convection Regimesmentioning

confidence: 99%

Thermal Evolution and Magnetic Field Generation in Terrestrial Planets and Satellites

Breuer¹,

Labrosse²,

Spohn³

2010

Space Sci Rev

Self Cite

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Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and Venus do not. Magnetic field data recorded at Ganymede have been interpreted as evidence of a self-generated magnetic field. The other icy Galilean satellites have magnetic fields induced in their subsurface oceans while Io and the Saturnian satellite Titan apparently are lacking magnetic fields of internal origin altogether.

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Regime classification and planform scaling for internally heated mantle convection

Cited by 13 publications

References 82 publications

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

Rocky super-Earth interiors

Thermal Evolution and Magnetic Field Generation in Terrestrial Planets and Satellites

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