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| Titel |
When can we assume Lagrangian stationarity? |
| VerfasserIn |
N. Suciu, C. Vamoş, H. Vereecken, K. Sabelfeld, P. Knabner |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250022247
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| Zusammenfassung |
| The statistical stationarity in space of the Lagrangian velocity and the translation-invariance
of the ensemble average Green function are often key assumptions in stochastic modelling of
transport in natural porous media. We show that the two statements are equivalent and hold
true when the Eulerian velocity field is statistically homogeneous and the transport
equations admit unique solutions. Sufficiently smooth velocity samples that guarantee
unique solutions are ensured by the existence of the derivatives of the correlation
functions at the origin, as for instance in case of Gaussian correlations. These sufficient
conditions can hardly be relaxed and are very close to the necessary conditions. Random
velocity fields with exponential correlations obviously do not fulfill the sufficient
sample-smoothness conditions. Numerical approximations of such fields also show their
lack of smoothness and simulations of transport indicate dependence on initial
conditions of the ensemble average Lagrangian velocity and Green function, i.e.
statistical inhomogeneity. Therefore, the question whether Lagrangian stationarity
can be assumed in case of exponentially correlated fields remains a challenging
issue. |
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