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| Titel |
A benchmark comparison of numerical topography: what are suitable sticky-air parameters? |
| VerfasserIn |
Fabio Crameri, Susanne Buiter, Thibault Duretz, Taras Gerya, Gregor Golabek, Boris Kaus, Robert Orendt, Harro Schmeling, Paul Tackley |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250052716
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| Zusammenfassung |
| Topography is a direct observable of the interaction between the Earth’s internal and external
dynamics. Therefore, it is important for numerical models of lithospheric deformation to
compute topography accurately. Earth’s surface is a so-called free surface, which means that
both normal and shear stress should vanish at this interface. It has been shown that
correct treatment of the Earth’s surface as a free surface can have a significant effect
in models of lithospheric and mantle dynamics (Zhong et al., 1996, Kaus et al.,
2008; Kaus et al., 2010). However, a true free surface is computationally expensive
which is why most mantle convection simulations until now treat the surface as a
free-slip boundary. For these models, topography is computed directly from normal
stresses.
A free surface approximation, the so-called ”sticky-air”, has recently gained interest in
the geodynamic community. This method requires the addition of a fluid layer in the model
domain while retaining the computational advantage of a free-slip top boundary. The fluid
layer is a proxy for air (or water) and should, therefore, have a near-zero density and a
viscosity, which is several orders of magnitude lower than the lithosphere viscosity. The
interface between material markers defining the crust and the air has been shown to behave
similar to a true free surface (Zaleski and Julien, 1992; Gerya and Yuen, 2003b; Schmeling et
al., 2008; Quinquis et al., 2011). Sufficiently small normal stress at the surface is ensured
by the physical properties of the weak layer (i.e., the low values for density and
viscosity).
We present a theoretical background that provides the physical conditions under which
the sticky-air approach is a valid approximation of a true free surface. We evaluate two cases
that characterise the evolution of topography on different timescales: (1) relaxation of a
sinusoidal perturbation and (2) topography changes above a rising sphere. We quantitatively
compare topographies for five different numerical codes (using finite difference and finite
element techniques) and for several different topography calculation methods (a. direct
calculation of topography from normal stress, b. body-fitting methods allowing for meshing
the topography, c. Lagrangian tracking of the topography on an Eulerian grid). It is found
that the sticky air approach works fine as long as the term (ηst/ηch)/(hst/hch)3 is
sufficiently small, where ηst and hst are the viscosity and thickness of the sticky air
layer, and ηch and hch are the characteristic viscosity and length scale of the model,
respectively.
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