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Title (Primary) Macrodispersivity for transport in arbitrary nonuniform flow fields: asymptotic and preasymptotic results
Author Lunati, I.; Attinger, S.; Kinzelbach, W.;
Journal Water Resources Research
Year 2002
Department CHS;
Volume 38
Issue 10
Language englisch;
Keywords homogenization theory; two-scale analysis; nonuniform flow; upscaling; macrodispersivity
Abstract We use homogenization theory to investigate the asymptotic macrodispersion in arbitrary nonuniform velocity fields, which show small-scale fluctuations. In the first part of the paper, a multiple-scale expansion analysis is performed to study transport phenomena in the asymptotic limit ? « 1, where ? represents the ratio between typical lengths of the small and large scale. In this limit the effects of small-scale velocity fluctuations on the transport behavior are described by a macrodispersive term, and our analysis provides an additional local equation that allows calculating the macrodispersive tensor. For Darcian flow fields we show that the macrodispersivity is a fourth-rank tensor. If dispersion/diffusion can be neglected, it depends only on the direction of the mean flow with respect to the principal axes of anisotropy of the medium. Hence the macrodispersivity represents a medium property. In the second part of the paper, we heuristically extend the theory to finite ? effects. Our results differ from those obtained in the common probabilistic approach employing ensemble averages. This demonstrates that standard ensemble averaging does not consistently account for finite scale effects: it tends to overestimate the dispersion coefficient in the single realization.
ID 5770
Persistent UFZ Identifier http://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=5770
Lunati, I., Attinger, S., Kinzelbach, W. (2002):
Macrodispersivity for transport in arbitrary nonuniform flow fields: asymptotic and preasymptotic results
Water Resour. Res. 38 (10), 1187