Numerical models of convection in the upper mantle

Houston, M. H.; Bremaecker, J. Cl. De

doi:10.1029/jb080i005p00742

Cited by 61 publications

(24 citation statements)

References 36 publications

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“…Thus Parmentier, Turcotte & Torrance (1976) found that a stressdependent rheology had very little effect on the flow pattern, while flow patterns with depth or temperature dependent viscosity calculated by Torrance & Turcotte (1971) and Houston & De Bremaecker (1975) were significantly affected, but also had internal variations of viscosity of two or more orders of magnitude. It is notable that Houston & De Bremaecker (1975) calculated cells with large aspect ratios (width to depth) in situations with high viscosities near the upper boundary, which was free to niove. Coinparisoil with calculations with imposed moving upper boundaries (Richter 1973;Parmentier 1976).…”

Section: Discussionmentioning

confidence: 94%

Whole-mantle convection and plate tectonics

Davies¹

1977

Geophys J Int

133

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It seems unlikely that the lower mantle is not involved in motions related to plate tectonics. The evidence relating to several alleged obstacles to lower-mantle convection is reviewed. The evidence for a chemical composition difference between the upper and lower mantle is not compelling. There now seems to be good evidence that the viscosity of the mantle is fairly uniform, contrary to a widely-held view, except possibly in the oceanic upper mantle. Phase changes may locally enhance or retard thermal convection, but are unlikely to prevent it. It is not necessary to assume that descending lithospheric slabs cannot penetrate below 700 km depth in order to explain the distribution and source mechanisms of deep earthquakes. Other recent seismic evidence suggests deep-mantle heterogeneities which may be related to large-scale flow.The behaviour of some simple layered-fluid models is analysed to show the effect of viscosity contrasts. The results indicate that the lower mantle would have to be 10000 times more viscous than the upper mantle in order to confine thermal convection to the upper mantle. The lower mantle would have to be at least 1000 times more viscous than the upper mantle in order to exclude viscous flow entrained by the moving plates. Alternatively, a shallow low-viscosity hyer would have to be about 10 000 times less viscous than the underlying mantle for the 'return' flow to be confined to it. These and other results indicate that only extreme viscosity contrasts (arising from non-linear or temperature-dependent rheology, for instance, as well as from different physical states) significantly affect large-scale flow patterns, and that flow patterns are strongly affected by moving boundaries.A version of whole-mantle thermal convection is proposed which seems to be capable of explaining the main features of plate tectonics: the buoyancy forces are concentrated in, but not confined to, the descending lithospheric slabs. Descending slabs would then cause their attached plates to move rapidly, as in the Elsasser model. The flow entrained by the fast plates would dominate the flow pattern in the mantle: convection cells under fast plates would be amplified; those under other plates would have smaller amplitudes and would fit between the fast cells. This model can qualitatively account for 460 G. F. Davies the large horizontal scale of the plates, the imperfect correlation between plate speed and the amount of attached descending slab, the motion of plates with 110 attached slab, and the opening of the Atlantic in particular. The model may provide a mechanism for the cyclic aggregation and dispersal of continents. The large-scale flow probably has smaller scale complications, especially in the upper mantle, and may be intrinsically unsteady. Narrow ascending thermal plumes could probably be incorporated into this model.

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Section: Discussionmentioning

confidence: 94%

Whole-mantle convection and plate tectonics

Davies¹

1977

Geophys J Int

133

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“…The widely used iterative techniques (e.g. Richter 1973;McKenzie :1977;Lux, Davies & Thomas 1979;Davies 1986) start with an estimate for ox (or SZx) on the boundaries and then solve the second-order equations separately, using Dirichlet boundary conditions on each. From this interim solution an improved estimate for w, (or SZ,) on the boundaries is then obtained by enforcing the zero-gradient condition on V x (or Yx).…”

Section: Solution Algorithm 11: Rigid Boundariesmentioning

confidence: 99%

Boundary Conditions and Efficient Solution Algorithms For the Potential Function Formulation of the 3-D Viscous Flow Equations

Houseman

1990

Geophysical Journal International

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S U M M A R Y For incompressible viscous creeping flows that occur in a number of geophysical situations, the velocity field may be expressed as the curl of a vector potential function, the use of which allows the momentum equation to be written as a biharmonic equation. The 3-D Cartesian formulation for a constant viscosity fluid is summarized here with special reference to two important types of boundary condition: the stress-free boundary (with zero normal velocity and zero tangential stress) and the rigid boundary (with all components of velocity zero). Fast algorithms for inversion of the biharmonic operator with all boundaries stress-free are well established. There also exists a fast method for the solution of the biharmonic equation with a parallel pair of rigid boundaries with the other boundaries stress-free. This method has not previously been applied, but it is a relatively straightforward extension of the Fourier transform based algorithm for the stress-free problem, using an analytical solution to enforce the required boundary conditions for each horizontal harmonic component. The method is easily vectorized and allows solutions to be obtained that compare very favourably in accuracy and solution time with those for the stress-free problem. The errors are of comparable magnitude given the differing harmonic content required by the boundary conditions, and the solution requires between 20 per ce-t (for a 3-D problem) and 30 per cent (for a 2-D problem) more processing time than does the solution of a comparable stress-free problem.

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“…An important addition regarding 2‐D mantle convection calculations is the inclusion of temperature dependent viscosity. The calculations done by Houston & De Bremaecker (1975), Parmentier et al (1976), Daly (1980), Jacoby & Schmeling (1982), Tackley (1993), Christensen (1984), Moresi & Solomatov (1995) and Ratcliff et al (1997) all included temperature dependent viscosity. Moresi & Solomatov (1995) reveal three different convection regimes in fluids with variations in viscosity.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional mantle convection simulations using an internal state variable model: the role of a history dependent rheology on mantle convection

Sherburn¹,

Horstemeyer²,

Bammann³

et al. 2011

Geophysical Journal International

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S U M M A R YWe apply the Bammann inelastic internal state variable model (BIISV) to a mantle convection code TERRA2D to investigate the influence of a history dependent solid mechanics model on mantle convection. We compare and contrast the general purpose BIISV model to the commonly used power-law model. We implemented the BIISV model using a radial return algorithm and tested it against previously published mantle convection simulation results for verification. Model constants for the BIISV are used based on experimental stress-strain behaviour found in the literature. After implementation we give illustrative simulation examples were the BIISV produces hardened areas on the cold thermal boundary layer that the powerlaw model cannot produce. The hardened boundary layers divert material downward giving a plausible reason for the current subduction zones that are present on the Earth.

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Numerical models of convection in the upper mantle

Cited by 61 publications

References 36 publications

Whole-mantle convection and plate tectonics

Whole-mantle convection and plate tectonics

Boundary Conditions and Efficient Solution Algorithms For the Potential Function Formulation of the 3-D Viscous Flow Equations

Two-dimensional mantle convection simulations using an internal state variable model: the role of a history dependent rheology on mantle convection

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