Theoretical Mantle Dynamics

Ribe, Neil M.

doi:10.1017/9781316795897

Cited by 7 publications

(8 citation statements)

References 327 publications

(512 reference statements)

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“…Following Ribe (2018), we refer to a viscous shell as a sheet. Our model lithosphere can be considered as a shallow sheet if its “midsurface departs from a reference plane by an amount much smaller than its principal radii of curvature” (Ribe, 2018). To estimate the midsurface departure, we consider the chord, with length C , as the reference plane and the arc, with length A , as the curved midsurface (Figure 2a).…”

Section: Modelmentioning

confidence: 99%

“…Therefore, the lithosphere in our model can be considered as a shallow sheet. Consequently, the differences in stress and velocity between a flat lithosphere and a curved lithosphere are likely in the order of the value of H / L ≈ 0.1 (e.g., Ribe, 2018). Hence, we do not expect significant differences between the results of a flat and curved lithosphere.…”

Section: Modelmentioning

confidence: 99%

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3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

Macherel,

Räss,

Schmalholz

2024

Geochem Geophys Geosyst

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Understanding stresses is crucial for geodynamics since they govern rock deformation and metamorphic reactions. However, the magnitudes and distribution of crustal stresses are still uncertain. Here, we use a 3D numerical model in spherical coordinates to investigate stresses and velocities that result from lateral crustal thickness variations around continental plateaus like those observed for the Tibetan plateau. We do not consider any far‐field deformation so that the plateau deforms by horizontal dilatation and vertical thinning. We assume viscous creep, a simplified plateau geometry, and simplified viscosity and density distributions to couple the numerical results with a scaling analysis. Specifically, we study the impact of the viscosity ratio between crust and lithospheric mantle, a rectangular plateau corner, a stress‐dependent power‐law flow law and Earth's double curvature on the crustal stress field and horizontal velocities. Two orders of magnitude variation in crustal and lithospheric mantle viscosities change the maximum crustal differential stress only by a factor of ≈2. We derive simple analytical estimates for the crustal deviatoric stress and horizontal velocity which agree to first order with 3D numerical calculations. We apply these estimates to calculate the average crustal viscosity in the eastern Tibetan plateau as ≈1022 Pa · s. Furthermore, our results show that a corner strongly affects the stress distribution, particularly the shear stresses, while Earth's curvature has a minor impact on the stresses. We further discuss potential implications of our results to strike‐slip faulting and fast exhumation around the Tibetan plateau's syntaxes.

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Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

Macherel,

Räss,

Schmalholz

2024

Geochem Geophys Geosyst

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“…They determined the existence of an analytical solution for a particular class of non‐Newtonian fluid. Ribe [ 3 ] also studied the self‐similarity in a system with flow and heat transfer. This study identified two regions susceptible to self‐similar transformation depending on the Raleigh number.…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling of extrusion through a Garvey die: Cost and performance

Stradi‐Granados

2023

SPE Polymers

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Modeling of complex systems requires large and expensive computational systems. Costs and processing time can be reduced by more than half in a wellmanaged cloud environment. Modeling the flow of ethylene propylene diene monomer (EPDM) through a Garvey die was achieved by employing the latest cloud computer technology commercially available at a modest cost. The description of the stress-strain behavior for EPDM was done using the Otswald-de Waele model. The results demonstrate that at higher velocities, the flow lines do not follow a smooth profile upon exiting the die, which indicates instabilities that may affect on the finished surface. Prediction of extrudate flow instabilities gives a computational option to make an initial estimate of permissible extrusion speeds.

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“…Beyond the governing equations, the Stokes-Rayleigh analogy also applies to the solutions to boundary value problems if the boundary conditions themselves are analogous [Ribe, 2018]. In the case of interest here, the Stokes-Rayleigh analogy predicts for an incompressible body that elastic isostasy with zero surface (resp.…”

Section: Stokes-rayleigh Analogymentioning

confidence: 99%

Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

Beuthe

2020

Preprint

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In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper I gave a general formulation of Airy isostasy as a loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two flavours of which are the constant load applied at a specific time and the constant shape maintained by addition or removal of material at the compensation depth. Whereas the former model has no elastic analog, the latter is equivalent to elastic isostasy with zero deflection at the surface, which was shown in Paper I to be dual to minimum stress isostasy. Viscoelastic and viscous approaches are completely equivalent. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Analytical formulas for the isostatic ratios of an incompressible body with three homogeneous layers are given in complementary software.

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Theoretical Mantle Dynamics

Cited by 7 publications

References 327 publications

3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

Modeling of extrusion through a Garvey die: Cost and performance

Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

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