Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Yao, C.; Deschamps, Frédéric; Lowman, J. P.; Sanchez-Valle, Carmen; Tackley, P. J.

doi:10.1002/2014je004653

Cited by 28 publications

(73 citation statements)

References 35 publications

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“…Jarvis et al () explored the influence of relative core size on temperature and convective planform in isoviscous systems and found convection in cold spherical shells characterized by a single plume rising from the core when f is 0.3 or less. Yao et al () reported similar planforms with viscosity contrasts up to 10 5 but relatively low effective Rayleigh numbers. These authors derived parameterizations for the interior temperature and heat flux in variable core size spherical shell SLC (Yao et al, ) heated solely by an isothermal core.…”

Section: Introductionmentioning

confidence: 82%

The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

et al. 2018

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Convection in terrestrial bodies occurs within spherical shells described by the ratio, f, of their bounding radii. Previous studies that have modeled convection with a temperature‐dependent viscosity noted the strong effect of f on transition to the stagnant‐lid regime. Here we analyze stagnant‐lid convection in 2‐D and 3‐D systems with curvatures including relatively small‐core shells (f as small as 0.2) as well as in thin shell and plane‐layer cases. Several peculiarities of convection in a strongly temperature‐dependent viscosity fluid are identified for both high and low curvature systems. We demonstrate that effective Rayleigh numbers may differ by orders of magnitude in systems with different curvatures, when all other parameters are maintained at fixed values. Furthermore, as f is decreased, the nature of stagnant‐lid convection in small‐core bodies shows a divergence in the temperature and velocity fields found for 2‐D annulus and 3‐D spherical shell systems. In addition, substantial differences in the behavior of thin shell (f = 0.9) and plane‐layer (Cartesian geometry) models occur in both 2‐D and 3‐D, indicating that the latter (emulating a toroidal topology rather than spherical) may be inappropriate approximations for modeling variable viscosity convection in thin spherical shells. Our findings are especially relevant to understanding and accurately modeling the thermal structure that may exist in bodies characterized by thin shells (e.g., f = 0.9) or relatively small cores, such as shells comprising the Galilean satellites and other moons.

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Section: Introductionmentioning

confidence: 82%

The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

et al. 2018

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“…Therefore, even lower‐reference viscosities or activation energies might be required. On the other hand, small cores tend to promote the formation of low‐degree (possibly degree‐one) structures in 3‐D isochemical thermal convection (Guerrero et al, ; Yao et al, ). The IBC overturn is driven by a compositional instability, which, as previously discussed in this section, is likely to grow according to a small wavelength comparable to the IBC thickness.…”

Section: Discussionmentioning

confidence: 99%

Overturn of Ilmenite‐Bearing Cumulates in a Rheologically Weak Lunar Mantle

Tosi

Schwinger

et al. 2019

JGR Planets

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The crystallization of the lunar magma ocean (LMO) determines the initial structure of the solid Moon. Near the end of the LMO crystallization, ilmenite‐bearing cumulates (IBC) form beneath the plagioclase crust. Being denser than the underlying mantle, IBC are prone to overturn, a hypothesis that explains several aspects of the Moon's evolution. Yet the formation of stagnant lid due to the temperature dependence of viscosity can easily prevent IBC from sinking. To infer the rheological conditions allowing IBC to sink, we calculated the LMO crystallization sequence and performed high‐resolution numerical simulations of the overturn dynamics. We assumed a diffusion creep rheology and tested the effects of reference viscosity, activation energy, and compositional viscosity contrast between IBC and mantle. The overturn strongly depends on reference viscosity and activation energy and is facilitated by a low IBC viscosity. For a reference viscosity of 1021 Pa s, characteristic of a dry rheology, IBC overturn cannot take place. For a reference viscosity of 1020 Pa s, the overturn is possible if the activation energy is a factor of 2–3 lower than the values typically assumed for dry olivine. These low activation energies suggest a role for dislocation creep. For lower‐reference viscosities associated with the presence of water or trapped melt, more than 95% IBC can sink regardless of the activation energy. Scaling laws for Rayleigh‐Taylor instability confirmed these results but also showed the need of numerical simulations to accurately quantify the overturn dynamics. Whenever IBC sink, the overturn occurs via small‐scale diapirs.

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“…Compared to the isoviscous cases, therefore, the internal temperature is generally higher (Figure b), and so is the internal heating ratio; the values of ξ are ∼0.47 and ∼0.76, respectively, for H ∗ of only 3 and 6. For purely basal heating and purely internal heating, various scaling relations are available [e.g., Moresi and Solomatov , ; Solomatov and Moresi , ; Reese et al , ; Deschamps and Lin , ; Yao et al , ], and it is straightforward to design a simulation with a desired combination of surface heat flux and internal temperature. For mixed heating, such relations are yet to be developed, and it requires some trial and error to control surface heat flux, internal temperature, and internal heating ratio.…”

Section: Basicsmentioning

confidence: 99%

Pitfalls in modeling mantle convection with internal heat production

Korenaga

2017

JGR Solid Earth

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The mantle of the Earth, and probably of other terrestrial planets as well, is heated from below and within. The heating mode of mantle convection is thus mixed heating, and it is also time dependent because the amount of heat‐producing isotopes in the mantle is steadily decreasing by radioactive decay and because the basal heat flux originating in the cooling of the core can vary with time. This mode of transient mixed heating presents its own challenges to the study of mantle convection, but such difficulties are not always appreciated in the recent literature. The purpose of this tutorial is to clarify the issue of heating mode by explaining relevant concepts in a coherent manner, including the internal heating ratio, the Urey ratio, secular cooling, and the connection between the thermal budget of the Earth and the geochemical models of the Earth. The importance of such basic concepts will be explained with some illustrative examples in the context of the thermal evolution of the Earth, and a summary of common pitfalls will be provided, with a possible strategy for how to avoid them.

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Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Cited by 28 publications

References 35 publications

The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

Overturn of Ilmenite‐Bearing Cumulates in a Rheologically Weak Lunar Mantle

Pitfalls in modeling mantle convection with internal heat production

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