 |
| Titel |
Role of viscoelasticity in mantle convection models |
| VerfasserIn |
Vojtech Patocka, Ondrej Cadek, Paul Tackley |
| Konferenz |
EGU General Assembly 2015
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250106135
|
| Publikation (Nr.) |
 EGU/EGU2015-5788.pdf |
|
|
|
|
|
| Zusammenfassung |
| A present limitation of global thermo-chemical convection models is that they assume a
purely viscous or visco-plastic flow law for solid rock, i.e. elasticity is ignored. This may not
be a good assumption in the cold, outer boundary layer known as the lithosphere, where
elastic deformation may be important. Elasticity in the lithosphere plays at least two roles: It
changes surface topography, which changes the relationship between topography and
gravity, and it alters the stress distribution in the lithosphere, which may affect
dynamical behaviour such as the formation of plate boundaries and other tectonics
features.
A method for adding elasticity to a viscous flow solver to make a visco-elastic flow
solver, which involves adding advected elastic stress to the momentum equation and
introducing an "effective" viscosity has been proposed (e.g. Moresi, 2002). The proposed
method is designed primarily for a regional-scale numerical model which employs tracers for
advection and co-rotation of the stress field. In this study we test a grid-based version of
the method in context of thermal convection in the Boussinesq approximation. A
simple finite difference/volume model with staggered grid is used, with the aim
to later use the same method to implement viscoelasticity into StagYY (Tackley,
2008).
The main obstacle is that Maxwell viscoelastic rheology produces instantaneous
deformation if instantaneous change of the driving forces occurs. It is not possible to model
such deformation in a velocity formulated convection model, as velocity undergoes a
singularity for an instantaneous deformation. For a given Rayleigh number there exists a
certain critical value of the Deborah number above which it is necessary to use a thermal time
step different from the one used in viscoelastic constitutive equation to avoid this numerical
instability from happening. Critical Deborah numbers for various Rayleigh numbers are
computed. We then propose a method to decouple the thermal and constitutive
equations in a way more suitable for global studies, which is different from the
method refered to earlier. The computational domain is expected to be composed of
two parts: One in which elastic effects are important and where material does not
move significantly within one elastic time step and one where elastic effects are not
important, where material is allowed to move across many cells within one elastic time
step.
Local accumulation of stress in viscoelastic simulations is observed, suggesting elasticity
could e.g. trigger plasticity in realistic cases.
References
Moresi L., Dufour F., Mühlhaus H.-B., 2003: A Lagrangian integration point finite element
method for large deformation modeling of viscoelastic geomaterials, Journal of
Computational Physics, 184 (2003), 476 - 497
Tackley P., 2008: Modelling compressible mantle convection with large viscosity contrasts in
a three-dimensional spherical shell using the yin-yang grid, Physics of the Earth and
Planetary Interiors, 171 (2008), 7-18 |
|
|
|
|
|
|