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The Quarterly Journal of Mechanics and Applied Mathematics 1992 45(1):1-24; doi:10.1093/qjmam/45.1.1
© 1992 by Oxford University Press
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A BOUNDARY-LAYER PROBLEM IN FRESH-SALT GROUNDWATER FLOW

C. J. VAN DUIJN and L. A. PELETIER

( Department of Mathematics, Delft University of Technology Julianalaan 132, 2628 BL Delft, The Netherlands
Mathematical Institute, Leiden University The Netherlands )

In this paper we investigate the boundary layer which arises between the parallel flow of fresh and salt groundwater as occurs in vertical aquifers. It is caused by small molecular diffusion and transversal dispersion brought about by the porous environment. A self-similar transformation leads to a variant of the Falkner-Skan equation. Existence, uniqueness and various properties of the solution, such as monotonicity and asymptotic behaviour, are established and the influence of the ratio of molecular diffusion to transversal dispersion is analysed. Some numerical results are presented.


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