Abstract
Assessment of recharge zones of strategic aquifers in Northern Oman calls for quantification of groundwater hydraulics in alluvial fans with a subjacent bedrock of various geometry. Unlike standard analytical solutions to a 2-D unconfined flow over a tilted bedrock and a common Dupuit–Forchheimer approximation we derive novel analytical solutions for subjacent confining layer of a non-constant slope or a bedding inconformity. We use a genuine 2-D flow model, conformal mappings and inverse boundary-value problems methods. For flow over an arbitrary corner the vertex is either a stagnation point or point of infinite Darcian velocity. The hodograph domain (a circular triangle) is mapped onto a complex potential strip via an auxiliary half-plane. A non-planar aquifuge is also reconstructed as a streamline, along which an additional “control” boundary condition holds (pore pressure as a function of an auxiliary variable).
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Acknowledgments
Support by the grant SR/SCI/ETHS/11/01, His Majesty Research Trust Fund (Oman) and by Russian Foundation of Basic Research grant N 12-01-97015-r\(\backslash \)_povolgh’e\(\backslash \)_a is appreciated.
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Kacimov, A., Obnosov, Y., Abdalla, O. (2014). New Analytical Solutions for Phreatic Darcian Flows Over Non-Planar Bedrocks. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_91
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DOI: https://doi.org/10.1007/978-3-642-32408-6_91
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