<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations. In particular, this corresponds to the superposition of independent random velocity fields with increasing integral scales proposed as model for evolving scale heterogeneity of natural porous media [Gelhar, L. W. Water Resour. Res. 22 (1986), 135S-145S]. Monte Carlo simulations of transport in such multi-scale fields support the theoretical results and demonstrate the approach to superdiffusive behavior as the number of superposed scales increases.</p></abstract>

Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations. In particular, this corresponds to the superposition of independent random velocity fields with increasing integral scales proposed as model for evolving scale heterogeneity of natural porous media [Gelhar, L. W. Water Resour. Res. 22 (1986), 135S-145S]. Monte Carlo simulations of transport in such multi-scale fields support the theoretical results and demonstrate the approach to superdiffusive behavior as the number of superposed scales increases.

Solute transport in aquifers with evolving scale heterogeneity

Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen, Germany

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Str. Fantanele 57, 400320 Cluj-Napoca,

Faculty for Chemistry and Earth sciences, University of Jena, Burgweg 11, 07749 Jena, Germany

Department Computational Hydrosystems, UFZ Centre for Environmental Research, Permoserstraß 15 04318 Leipzig,

Department of Mathematics, University of Bergen, Allegaten 41, 5020 Bergen,

Institute of Bio- and Geosciences Agrosphere (IBG-3) Forschungszentrum Jlich IBG-3, Wilhelm-Johnen-Straß, 52428 Jlich,

Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Solute transport in aquifers with evolving scale heterogeneity"}

Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in...

Solute transport in aquifers with evolving scale heterogeneity

Published Online: Apr 22, 2017

Page range: 167 - 186

Received: Dec 01, 2014

Accepted: Feb 01, 2015

DOI: https://doi.org/10.1515/auom-2015-0054

Keywords
Porous media, Random fields, transport, random walk

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Solute transport in aquifers with evolving scale heterogeneity

Published Online: Apr 22, 2017

Page range: 167 - 186

Received: Dec 01, 2014

Accepted: Feb 01, 2015

DOI: https://doi.org/10.1515/auom-2015-0054

KeywordsPorous media, Random fields, transport, random walk

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Porous media, Random fields, transport, random walk