Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles

Shahnas, M. H.; Lowman, J. P.; Jarvis, Gary T.; Bunge, Hans‐Peter

doi:10.1016/j.pepi.2008.04.007

Cited by 28 publications

(25 citation statements)

References 24 publications

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“…The fact that increasing the curvature of the cylinder (decreasing the ratio of inner to outer radii) leads to a decrease in heat flux has been previously demonstrated in a systematic numerical study of Jarvis [1993]. An analogous effect of curvature on heat transport properties has also been demonstrated in models of mantle convection in three-dimensional spherical geometry [Hosein Shahnas et al, 2008;Deschamps et al, 2010]. However, Hernlund and Tackley [2008] have pointed out that using such small inner radius for cylindrical geometry as proposed by van Keken [2001] leads to an artificial "crowding" of thermal and compositional structures at the base of the mantle.…”

Section: A2 Cylindrical Geometrymentioning

confidence: 71%

Survival of LLSVPs for billions of years in a vigorously convecting mantle: Replenishment and destruction of chemical anomaly

et al. 2015

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We study segregation of the subducted oceanic crust (OC) at the core-mantle boundary and its ability to accumulate and form large thermochemical piles (such as the seismically observed Large Low Shear Velocity Provinces (LLSVPs)). Our high-resolution numerical simulations of thermochemical mantle convection suggest that the longevity of LLSVPs for up to three billion years, and possibly longer, can be ensured by a balance in the rate of segregation of high-density OC material to the core-mantle boundary (CMB) and the rate of its entrainment away from the CMB by mantle upwellings. For a range of parameters tested in this study, a large-scale compositional anomaly forms at the CMB, similar in shape and size to the LLSVPs. Neutrally buoyant thermochemical piles formed by mechanical stirring-where thermally induced negative density anomaly is balanced by the presence of a fraction of dense anomalous material-best resemble the geometry of LLSVPs. Such neutrally buoyant piles tend to emerge and survive for at least 3 Gyr in simulations with quite different parameters. We conclude that for a plausible range of values of density anomaly of OC material in the lower mantle-it is likely that it segregates to the CMB, gets mechanically mixed with the ambient material, and forms neutrally buoyant large-scale compositional anomalies similar in shape to the LLSVPs.

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Section: A2 Cylindrical Geometrymentioning

confidence: 71%

Survival of LLSVPs for billions of years in a vigorously convecting mantle: Replenishment and destruction of chemical anomaly

et al. 2015

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“…However, overall, significant changes in plateness and mobility are not observed for the factor of five increase in Ra T investigated. In contrast, as is the case for isoviscous convection (Deschamps et al, 2010;Shahnas et al, 2008;, for this Rayleigh number increase (with H fixed) the PCH increases significantly as Ra T is increased (by approximately 25% for the cases with higher Ra T ) in accord with a drop in the mean temperature. Figure 12 shows a snapshot from Model H30Y2e6 0 (7) with Ra T 510 9 ; d f 50:025 and Dg T 53:2310 6 , where the thermal viscosity contrast has been increased by an order of magnitude and Ra T is 10 9 .…”

Section: 1002/2017gc007266mentioning

confidence: 74%

The Sensitivity of Core Heat Flux to the Modeling of Plate‐Like Surface Motion

Langemeyer

Lowman

Tackley

2018

Geochem Geophys Geosyst

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The generation of a magnetic field and the presence of tectonic plates are fundamental aspects of Earth's evolution. Viable dynamic models of terrestrial mantle convection therefore require the existence of heat transport from the core and a surface characterized by piecewise uniform surface velocity domains (i.e., plates). To test the compatibility of these two requirements, we varied energy input, rheology, and compositional heterogeneity in more than 70 mantle convection simulations. Calculations are performed in a spherical annulus geometry. By systematic investigation, we demonstrate that Earth‐like core heat flux can be obtained with self‐consistent model plates. We find that, given an initial condition where model parameters are chosen to ensure a mobile surface, the mobility is not strongly influenced when H is varied by up to a factor of three. Consequently, in spherical models with steady core temperatures and internal heating rates, the latter quantity can be used to regulate core heat flow to fit within the bounds inferred for terrestrial values. In contrast, core heat flow is strongly sensitive to model yield stress. We systematically vary thermal viscosity contrast, an intrinsic depth‐dependent viscosity and the depth‐dependence of a stress‐dependent rheology and analyze how each factor affects both surface velocities and core heat flux. Finally, we show that the addition of an intrinsically dense component comprising 5% or less of the mantle volume does not affect surface mobility or plateness, although it can have a profound impact on heat loss from the core.

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“…For an isoviscous, 3D-Cartesian system heated from below, these two layers are geometrically and dynamically symmetric. Both spherical geometry and internal heating break this symmetry, and a have strong influence on the properties of the top and bottom TBLs, resulting in parameterizations for average temperature and heat flux that explicitly depend on h and f [Sotin and Labrosse, 1999;Moore, 2008;Shahnas et al, 2008, Deschamps et al, 2010. Even when rescaled with equation (4), the average temperatures observed in these studies do not fit along a power law of the Rayleigh-Roberts number and still have a strong dependence on h and f.…”

Section: Comparison With Mixed Heated Spherical Shellsmentioning

confidence: 95%

“…This expression should satisfy two boundary conditions, corresponding to the average temperatures for pure bottom and volumetric heating, respectively. For pure bottom heating the average temperature, 〈T BH 〉, depends only on the shell curvature through the parameter f and goes to zero for f = 0 [Vangelov and Jarvis, 1994;Jarvis et al, 1995;Shahnas et al, 2008;Deschamps et al, 2010]. Here, we will assume that 〈T BH 〉 follows the law suggested by Deschamps et al [2010], f 2 /(1 + f 2 ).…”

Section: Comparison With Mixed Heated Spherical Shellsmentioning

confidence: 99%

“…where C is a parameter that depends on f. This additional dependency is needed to explain the data from numerical experiments with mixed heating [Shahnas et al, 2008;Deschamps et al, 2010], and may be related to the fact that the relative size of the top and bottom TBL strongly varies with f. With decreasing f, the average temperature tends to that for pure internal heating, i.e., it is dominated by the second term of the right-hand-side in equation (22). Following Deschamps et al [2010], we assumed that C depends linearly on f, C = (c 1 + c 2 f ), where c 1 and c 2 are two constants.…”

Section: Comparison With Mixed Heated Spherical Shellsmentioning

confidence: 99%

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High Rayleigh number thermal convection in volumetrically heated spherical shells

Deschamps

Yao²,

Tackley³

et al. 2012

J. Geophys. Res.

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[1] We conducted experiments of isoviscous thermal convection in homogeneous, volumetrically heated spherical shells with various combinations of curvature, rate of internal heating, and Rayleigh number. We define a characteristic temperature adapted to volumetrically heated shells, for which the appropriate Rayleigh number, measuring the vigor of convection, ishkk , where f is the ratio between the inner and outer radii of the shell. Our experiments show that the scenario proposed by Parmentier and Sotin (2000) to describe convection in volumetrically heated 3D-Cartesian boxes fully applies in spherical geometry, regardless of the shell curvature. The dynamics of the thermal boundary layer are controlled by both newly generated instabilities and surviving cold plumes initiated by previous instabilities. The characteristic time for the growth of instabilities in the thermal boundary layer scales as Ra VH À1/2, regardless of the shell curvature. We derive parameterizations for the average temperature of the shell and for the temperature jump across the thermal boundary layer, and find that these quantities are again independent of the shell curvature and vary as Ra VH À0.238 and Ra VH À1/4 , respectively. These findings appear to be valid down to relatively low values of the Rayleigh-Roberts number, around 10 5 .

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Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles

Cited by 28 publications

References 24 publications

Survival of LLSVPs for billions of years in a vigorously convecting mantle: Replenishment and destruction of chemical anomaly

Survival of LLSVPs for billions of years in a vigorously convecting mantle: Replenishment and destruction of chemical anomaly

The Sensitivity of Core Heat Flux to the Modeling of Plate‐Like Surface Motion

High Rayleigh number thermal convection in volumetrically heated spherical shells

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