Vertically integrated unconfined groundwater flow on sloping base

We consider unconfined flow in aquifers with a small sloping base, a magnitude of no more than a few percent at maximum and aim the analysis to large-scale regional modeling using analytic elements. We write the equations for the vertically integrated discharge, and find that the resulting two-dimen...

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Bibliographic Details
Published in:Journal of engineering mathematics 2024-06, Vol.146 (1), Article 21
Main Author: Strack, Otto D. L.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Aquifers
Computational Mathematics and Numerical Analysis
Discharge
Groundwater flow
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Theoretical and Applied Mechanics
Three dimensional flow
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Summary:We consider unconfined flow in aquifers with a small sloping base, a magnitude of no more than a few percent at maximum and aim the analysis to large-scale regional modeling using analytic elements. We write the equations for the vertically integrated discharge, and find that the resulting two-dimensional discharge vector is rotational, as opposed to the specific discharge vector. We propose an approximate model for describing three-dimensional flow in an aquifer with a sloping base, and apply the approach to cases of flow between two parallel rivers and flow with a well in an aquifer bounded by a long river. We apply Wirtinger calculus and are able to estimate the error due to the approximation.
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-024-10360-4