Optimalität und Selbstorganisation bei Fließprozessen im Grund- und Bodenwasser
Zusammenfassung der Projektergebnisse
Focus of this project was on preferential subsurface flow patterns derived from the principle of minimum energy dissipation. The idea behind these patterns is that the hydraulic conductivity depends on the porosity and that both properties are organized spatially in such a way that the total energy dissipated by the water is minimized. Such flow patterns are characterized by strong variations in hydraulic parameters at small scales, which make their numerical treatment challenging. A large part of the project was devoted to improving the numerical treatment of such flow patterns. As a major achievement, a new, fully implicit scheme was developed. This scheme can be applied to a large class of linear problems on a tree-like topology, which means that each grid cell must deliver its discharge to a single flow target. This scheme turned out to be very efficient and also useful in the field of landform evolution modeling. As an alternative approach, spectral theory was formulated for two-dimensional aquifers with an arbitrary spatial distribution of the hydraulic properties. This approach is well-suited for investigating properties of such aquifers theoretically. Both approaches are, however, not applicable to nonlinear problems, e.g., to unconfined sloping aquifers with preferential flow patterns. A preliminary extension towards unconfined sloping aquifers was also developed, but has not yet been tested thoroughly. Concerning the dynamics, a nontrivial scaling behavior with the size of the aquifer and a finite rise time are the most striking results. Over long periods of drought, discharges of springs typically decrease exponentially, whereby the respective e-folding time depends on the hydraulic properties and on the catchment size. While it is typically expected that the e-folding recession time is proportional to the catchment size, its dependence on the catchment size is considerably weaker for preferential flow patterns with minimum energy dissipation. In turn, the response to an instantaneous recharge event shows a strong delay until the peak discharge is reached. After reaching the peak discharge, however, the discharge is quite close to that of a simple linear reservoir. Overall, these properties are quite far off from the properties of homogeneous aquifers, but also quite far off from what is often assumed for karst aquifers. So further research is needed with regard to the potential relation of preferential flow patterns with minimum energy dissipation to real aquifers.
Projektbezogene Publikationen (Auswahl)
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Flow recession behavior of dendritic subsurface flow patterns. Copernicus GmbH.
Strüven, Jannick & Hergarten, Stefan
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Flow recession behavior of dendritic subsurface flow patterns. Copernicus GmbH.
Strüven, Jannick & Hergarten, Stefan
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Flow recession behavior of preferential subsurface flow patterns with minimum energy dissipation. Copernicus GmbH.
Strüven, Jannick & Hergarten, Stefan
