Riesenkampf's vortex solution revisited for 2-D commingling of groundwater in a three-layered aquifer: Vertical-inclined-horizontal seepage in aquitard

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Using exact and explicit analytical solutions and MODFLOW simulations we show that downstream of an unconformity (transition from an aquifuge layer to a homogeneous aquitard) groundwater seeps at varying angles with respect to the layering. As a generalization of the Anderson (2003) two-layered composite, a steady, 2-D Darcian flow in a three-layered aquifer is studied. This flow is generated by different inlet piezometric heads in thick upper and lower strata and a cross-flow through an aquitard sandwiched between them. Analytically, a line vortex combined with a dipole at infinity describes commingling between the strata with refraction (continuity of head and normal flux component) along the upper and lower boundaries of the aquitard. The Fourier method by Riesenkampf (1940) gives explicit expressions for the specific discharge vector fields in the three media. MODFLOW models finite lengths composites of rectangular and octagonal shapes. The Dupuit–Forchheimer approximation is illustrated to oversimplify the flow topology.

Original languageEnglish
Pages (from-to)84-95
Number of pages12
JournalAdvances in Water Resources
Publication statusPublished - Jan 1 2019



  • 2-d flows versus Dupuit–Forchheimer approximation
  • Analytical solutions versus MODFLOW
  • Flow net-isotachs
  • Leaky layer versus leaky boundary
  • Line vortex superposed with dipole at infinity in a three-layered composite
  • Refracted specific discharge vector fields in an aquitard and two adjacent half-planes

ASJC Scopus subject areas

  • Water Science and Technology

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