Nusselt–Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of

Wolstencroft, Martin; Davies, John H.; Davies, David R.

doi:10.1016/j.pepi.2009.05.002

Cited by 39 publications

(32 citation statements)

References 44 publications

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“…Also, the result that <1∕3 brings into question results for 10.1002 normal stress modes where = 1∕3 is explicitly assumed for the convective zone [e.g., Foley et al, 2012;Valencia et al, 2007]. A value significantly smaller than 1/3 is in good agreement with various other studies with free-slip boundary conditions [e.g., Bercovici et al, 1989;Deschamps and Sotin, 2000, and references therein;Deschamps et al, 2010;Moore, 2008;Ratcliff et al, 1996;Sotin and Labrosse, 1999;Stamenković and Breuer, 2014;Wolstencroft et al, 2009;Yanagisawa and Yamagishi, 2005].…”

Section: The Limits Of Self-determined Boundary Layer Dynamicssupporting

confidence: 82%

“…Our 1-D scalings depends mainly on whether d = zz or d = zx but also on the thermal evolution parameters ( , , ): reasonable values for ( , , ) are 1∕5 < < 1∕3, 1∕3 < < 2∕3, and 0 < < 1∕6 and are in agreement with all 3-D an 2-D numerical simulations assuming reasonable mantle rock rheologies and theoretical constraints from evolution models for the Earth [e.g., Deschamps and Sotin, 2000, and references therein;Deschamps et al, 2010;Lenardic et al, 2006;Moore, 2008;Parmentier and Sotin, 2000;Ratcliff et al, 1996;Sotin and Labrosse, 1999;Stamenković and Breuer, 2014;Wolstencroft et al, 2009;Yanagisawa and Yamagishi, 2005;Zhong, 2005]. Values of much smaller than 1/5 or even negative [Korenaga, 2003] have not been confirmed by 2-D or 3-D numerical experiments to date, and as such, we did not explore them.…”

Section: A3 Model Parameters: ( )mentioning

confidence: 53%

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The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

2016

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We use 1‐D thermal history models and 3‐D numerical experiments to study the impact of dynamic thermal disequilibrium and large temporal variations of normal and shear stresses on the initiation of plate tectonics. Previous models that explored plate tectonics initiation from a steady state, single plate mode of convection concluded that normal stresses govern the initiation of plate tectonics, which based on our 1‐D model leads to plate yielding being more likely with increasing interior heat and planet mass for a depth‐dependent Byerlee yield stress. Using 3‐D spherical shell mantle convection models in an episodic regime allows us to explore larger temporal stress variations than can be addressed by considering plate failure from a steady state stagnant lid configuration. The episodic models show that an increase in convective mantle shear stress at the lithospheric base initiates plate failure, which leads with our 1‐D model to plate yielding being less likely with increasing interior heat and planet mass. In this out‐of‐equilibrium and strongly time‐dependent stress scenario, the onset of lithospheric overturn events cannot be explained by boundary layer thickening and normal stresses alone. Our results indicate that in order to understand the initiation of plate tectonics, one should consider the temporal variation of stresses and dynamic disequilibrium.

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Section: The Limits Of Self-determined Boundary Layer Dynamicssupporting

confidence: 82%

Section: A3 Model Parameters: ( )mentioning

confidence: 53%

The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

2016

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“…11a, the Nusselt number is displayed as a function of the effective Rayleigh number, for the different configurations with constant viscosity. The exponent for the EB series is 0.2406 similar to the value of 0.24 found by Iwase and Honda (1997), but different to the value of 0.28 obtained by Bercovici et al, 1989 andWolstencroft et al, 2009 in the three-dimensional spherical shell. It is interesting that, by moving to the compressible convection with constant thermodynamic property this value changes slightly to the 0.23.…”

Section: Constantcontrasting

confidence: 49%

Geoid and topography of Earth-like planets: A comparison between compressible and incompressible models for different rheologies

Shahraki

Schmeling

2013

Physics of the Earth and Planetary Interiors

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“…Using these equations we investigated the form of layered mantle convection for varying Ra and P . The simulations were undertaken using a benchmarked version of TERRA (Baumgardner, 1985;Bunge et al, 1997;Davies and Davies, 2009), which is able to model very high Ra in spherical geometry (Wolstencroft et al, 2009) shows the constant thermal gradient of a purely conductive regime. The dashed line in Part (B) shows the whole mantle convection thermal structure, illustrating the large temperature gradients at its boundaries.…”

Section: Methodsmentioning

confidence: 99%

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

Wolstencroft

Davies

2011

Solid Earth

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Abstract. We investigate the influence on mantle convection of the negative Clapeyron slope ringwoodite to perovskite and ferro-periclase mantle phase transition, which is correlated with the seismic discontinuity at 660 km depth. In particular, we focus on understanding the influence of the magnitude of the Clapeyron slope (as measured by the Phase Buoyancy parameter, P ) and the vigour of convection (as measured by the Rayleigh number, Ra) on mantle convection. We have undertaken 76 simulations of isoviscous mantle convection in spherical geometry, varying Ra and P . Three domains of behaviour were found: layered convection for high Ra and more negative P , whole mantle convection for low Ra and less negative P , and transitional behaviour in an intervening domain. The boundary between the layered and transitional domain was fit by a curve P = αRa β where α = −1.05, and β = −0.1, and the fit for the boundary between the transitional and whole mantle convection domain was α = −4.8, and β = −0.25. These two curves converge at Ra ≈2.5×10 4 (well below Earth mantle vigour) and P ≈ −0.38. Extrapolating to high Ra, which is likely earlier in Earth history, this work suggests a large transitional domain. It is therefore likely that convection in the Archean would have been influenced by this phase change, with Earth being at least in the transitional domain, if not the layered domain.

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Nusselt–Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of

Cited by 39 publications

References 44 publications

The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

The importance of temporal stress variation and dynamic disequilibrium for the initiation of plate tectonics

Geoid and topography of Earth-like planets: A comparison between compressible and incompressible models for different rheologies

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

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