Convection in three dimensions with surface plates: Generation of toroidal flow

Gable, Carl W.; O’Connell, Richard J.; Travis, B. J.

doi:10.1029/90jb02743

Cited by 177 publications

(142 citation statements)

References 44 publications

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“…Oceanic plate velocities are time-dependent and are dynamically determined using the total integrated shear stresses at the base of each plate (a force-balance calculation). This method of modeling plates and determining their velocities [Gable et al, 1991] has been shown to yield plate velocities and mean heat flux values in agreement with modeling methods that utilize rheologically defined plates [Koglin et al, 2005].…”

Section: Model Descriptionmentioning

confidence: 68%

“…[6] We model mantle convection using the hybrid finitedifference spectral-method code MC3D [Gable et al, 1991] to solve the equations for mass, momentum and energy conservation and use the extended Boussinesq approximation to include a depth-dependent mantle viscosity characterized by a factor of 36 increase from the upper mantle to the lower mantle.…”

Section: Model Descriptionmentioning

confidence: 99%

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Thermal response of the mantle following the formation of a “super‐plate”

Heron

Lowman

2010

Geophysical Research Letters

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[1] Evidence indicating that the mantle below Pangea was characterized by elevated temperatures supports the widely held view that a supercontinent insulates the underlying mantle. Implementing a 3D model of mantle convection featuring distinct oceanic and continental plates, we explore different effects of supercontinent formation on mantle evolution. We find that a halt in subduction along the margins of the site of the continental collision is sufficient to enable the formation of mantle plumes below a composite "super-plate" and that the addition of continental properties that contribute to insulation have little effect on sub-continental temperature. Our findings show that the mean temperature below a supercontinent surpasses that below the oceanic plates when the former is a perfect insulator but that continental thermal insulation plays only a minor role in the growth of sub-supercontinent mantle plumes. We suggest that the growth of a super-oceanic plate can equally encourage the appearance of underlying upwellings. Citation: Heron, P. J., and J. P. Lowman (2010), Thermal response of the mantle following the formation of a "super-plate," Geophys.

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Section: Model Descriptionmentioning

confidence: 68%

Section: Model Descriptionmentioning

confidence: 99%

Thermal response of the mantle following the formation of a “super‐plate”

Heron

Lowman

2010

Geophysical Research Letters

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“…Calculations were done using the Cartesian numerical code first written by Gable [1989] and Gable et al [1991] and later modified by Ito et al [ 1996] to incorporate variable viscosity. The numerical setup is illustrated in Figure 1.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Interaction of mantle plumes and migrating mid‐ocean ridges: Implications for the Galápagos plume‐ridge system

Ito¹,

Lin²,

Gable³

1997

J. Geophys. Res.

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109

129

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Abstract. We investigate the three-dimensional interaction of mantle plumes and migrating mid-ocean ridges with variable viscosity numerical models. Numerical models predict that alongaxis plume width W and maximum distance of plume-ridge interaction Xma x scale with (Q/U) 1/2, where Q is plume source volume flux and U is ridge full spreading rate. Both W and Xma x increase with buoyancy number li b which reflects the strength of gravitational-versus plate-driven spreading. Scaling laws derived for stationary ridges in steady-state with near-ridge plumes are consistent with those obtained from independent studies of Ribe [ 1996]. In the case of a migrating ridge, the distance of plume-ridge interaction is reduced when a ridge migrates toward the plume because of the excess drag of the faster moving leading plate and enhanced when a ridge migrates away from the plume because of the reduced drag of the slower moving trailing plate. Given the mildly buoyant and relatively viscous plumes investigated here, the slope of the lithospheric boundary and thermal erosion of the lithosphere have little effect on plume flow. From observed plume widths of the Galfipagos plume-migrating ridge system, our scaling laws yield estimates of Galfipagos plume volume flux of 5-16 x 106 km 3 m.y. -1 and a buoyancy flux of -2 x 103 kg s -1. Model results suggest that the observed increase in bathymetric and mantleBouguer gravity anomalies along Cocos Plate isochrons with increasing isochron age is due to higher crustal production when the Gal•pagos ridge axis was closer to the plume several million years ago. The anomaly amplitudes can be explained by a plume source with a relatively mild temperature anomaly (50ø-100øC) and moderate radius (100-200 km). Predictions of the along-axis geochemical signature of the plume suggest that mixing between the plume and ambient mantle sources may not occur in the asthenosphere but, instead, may occur deeper in the mantle possibly by entrainment of depleted mantle as the plume ascends from its source.

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“…Hager and O'Connell [1981] and Bunge and Richards [1996] imposed the velocity field at the surface. As opposed to this, Gable et al [1991] and Monnereau and Quéré [2001] prescribed only the initial plate geometry and introduced a coupling between plates and bulk convection supposing no direct interaction between the plates. There is a certain free space between the plates to allow an evolution of the plates.…”

Section: Plate-like Motions Of the Lithospherementioning

confidence: 99%

Mantle convection and evolution with growing continents

Walzer

Hendel

2008

J. Geophys. Res.

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[1] We present a three-dimensional spherical shell numerical model for chemical differentiation and redistribution of incompatible elements in a convective Earth's mantle heated mostly from within by U, Th, and K and slightly from below. The evolution-model equations guarantee conservation of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs 238 U-206 Pb, 235 U-207 Pb, 232 Th-208 Pb, and 40 K-40 Ar. The pressure-and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, s y . The lithospheric viscosity is partly imposed to mimic its increase by dehydration of oceanic lithosphere and other effects. Also, the asthenosphere is generated not only by the distribution of temperature and melting temperature, but essentially by the profiles of water solubility and water abundance. Therefore we introduced a radial viscosity profile factor describing that behavior. However, the focus of this paper is the episodic growth of continents and oceanic plateaus. As a complement, the differentiation generates the depleted MORB mantle (DMM) which predominates immediately beneath the lithosphere. Our continents are not artificially imposed on the surface of the spherical shell, but instead they evolve by the interplay between chemical differentiation and convection/mixing. No restrictions are imposed regarding number, size, form, and distribution of continents. However, oceanic plateaus that impinge upon a continent have to be united with it. This mimics the accretion of terranes. The numerical results show an episodic growth of the total mass of the continents and display a plausible time history for the laterally averaged surface heat flow, qob, and the Rayleigh number, Ra. We use our model to explore a moderate region of Ra-s y parameter space. We find Earth-like continent distributions in a central part of the Ra-s y space we explored. We identified a Ra-s y region where the calculated total continental volume is very close to the observed value; another Ra-s y region where the Urey number, Ur, is close to the accepted value; a third Ra-s y area where surface heat flow is very close to the present-day observed mean global heat flow using typical abundances of the heat-producing elements. It is remarkable that these different acceptable Ra-s y regions share a common overlap area, where Earth-like behavior is simultaneously fulfilled.Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Ra t , is relatively well predictable and the stochastic parts of the Ra t (t) curves are small. Regarding the time distribution of juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution, presumed that the initial conditions are given. Later on, the distribution of the continental growth episodes is increasingly stochastic. Independent of the varying individual runs, our model shows that the total mass of the presen...

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Convection in three dimensions with surface plates: Generation of toroidal flow

Cited by 177 publications

References 44 publications

Thermal response of the mantle following the formation of a “super‐plate”

Thermal response of the mantle following the formation of a “super‐plate”

Interaction of mantle plumes and migrating mid‐ocean ridges: Implications for the Galápagos plume‐ridge system

Mantle convection and evolution with growing continents

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