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| Titel |
Influence of bed surface changes on snow avalanche simulation |
| VerfasserIn |
Jan-Thomas Fischer, Dieter Issler |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250095513
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| Publikation (Nr.) |
 EGU/EGU2014-10971.pdf |
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| Zusammenfassung |
| Gravitational flows, such as snow avalanches, are often modeled employing the shallowness
assumption. The driving gravitational force has a first order effect on the dynamics
of the flow, especially in complex terrain. Under suitable conditions, erosion and
deposition during passage of the flow may change the bed surface by a similar
amount as the flow depth itself. The accompanying changes of local slope angle and
curvature are particularly significant at the side margins of the flow, where they
may induce self-channeling and levée formation. Generally, one ought to expect
visible effects wherever the flow depth and velocity are small, e.g., in deposition
zones.
Most current numerical models in practical use neglect this effect. In order to study
the importance of these effects in typical applications, we modified the quasi-3D
(depth-averaged) code MoT-Voellmy, which implements the well-known Voellmy
friction law that is traditionally used in hazard mapping: The bed shear stress is given
by
Ïiz(h,u) = –ui(μgh cosθ+ ku2),
||u||
(1)
with μ = O(0.1-¦0.5) and k = O(10-3-¦10-2) the dimensionless friction and drag
coefficients, respectively. The leading curvature effects, i.e., extra friction due to centrifugal
normal forces, are taken into account. The mass and momentum balances are solved by the
(simplified) method of transport on a grid whose cells are squares when projected onto the
horizontal plane. The direction of depth-averaging is everywhere perpendicular to the
topographic surface.
A simple erosion model is used. The erosion formula is based on the assumption that the
snow cover behaves as a perfectly brittle solid with shear strength Ïc, above which it
instantaneously fails. The erosion rate is derived from the balance of momentum across the
interface between bed and flow, where there is a discontinuity of the shear stress, which is
given by equation 1 just above the interface and by Ïc just below it according to the
assumptions. This immediately leads to the formula
2
qe = μgh-cosθ+-ku– Ïc-ÏfÎ (μgh cosθ+ ku2 - Ïc-Ïf).
||u||
(2)
We present numerical simulations with static and dynamic beds in two different cases.
First, an avalanche simulation on an inclined plane allows to study the occurring effects in
their most immediate form. This allows to study the influence of spatial resolution of the
computational grid. Second, we back-calculate a typical mid-size avalanche that was
measured and documented in 1993 at the Norwegian test site Ryggfonn. This case study
serves to test the relevance of including bed surface changes under conditions typical of
real-world applications. |
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