### Abstract

An analytical solution is obtained for steady 2-D potential seepage flow from a nonclogged and nonlined soil channel into a highly permeable porous layer, with phreatic surfaces tapering toward a horizontal interface with a subjacent low-permeable formation. Along this boundary, a vertical component of the Darcian velocity vector equals the formation saturated hydraulic conductivity. The image of the physical flow domain in the hodograph plane is a circular polygon, a triangle or digon in a limiting case of a "phreatic jet" impinging on the low-permeable substratum. The polygon is mapped onto an auxiliary half plane, where the complex physical coordinate and complex potential are reconstructed by the Polubarinova-Kochina method, i.e., by solution of a Riemann BVP. The seepage flow rate from the channel, free surfaces, and a saturated (water-logged) area are found for different thicknesses of the top layer, channel widths, and conductivity ratios of the two strata. In particular, the earlier results of Brock, Kirkham, and Youngs, which are based on a numerical solution, Dupuit-Forchheimer (DF) approximation, and approximate potential model, are confirmed in the full 2-D models. Sufficiently far from the channel, the phreatic surface and interface make a wedge. For a sufficiently deep substratum, three zones are analytically distinguished: an almost vertical 1-D descending flow, an almost wedge-configured 1-D flow, and an essentially 2-D zone in between, where neither a standard infiltration theory nor DF analysis are valid.

Original language | English |
---|---|

Pages (from-to) | 3093-3107 |

Number of pages | 15 |

Journal | Water Resources Research |

Volume | 51 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2015 |

### Fingerprint

### Keywords

- conformal mappings
- hodograph
- infiltration
- managed aquifer recharge
- perched aquifer
- Polubarinova-Kochina method

### ASJC Scopus subject areas

- Water Science and Technology

### Cite this

**An exact analytical solution for steady seepage from a perched Aquifer to a low-permeable sublayer : Kirkham-Brock's legacy revisited.** / Kacimov, A. R.; Obnosov, Yu V.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 51, no. 5, pp. 3093-3107. https://doi.org/10.1002/2014WR016304

}

TY - JOUR

T1 - An exact analytical solution for steady seepage from a perched Aquifer to a low-permeable sublayer

T2 - Kirkham-Brock's legacy revisited

AU - Kacimov, A. R.

AU - Obnosov, Yu V.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - An analytical solution is obtained for steady 2-D potential seepage flow from a nonclogged and nonlined soil channel into a highly permeable porous layer, with phreatic surfaces tapering toward a horizontal interface with a subjacent low-permeable formation. Along this boundary, a vertical component of the Darcian velocity vector equals the formation saturated hydraulic conductivity. The image of the physical flow domain in the hodograph plane is a circular polygon, a triangle or digon in a limiting case of a "phreatic jet" impinging on the low-permeable substratum. The polygon is mapped onto an auxiliary half plane, where the complex physical coordinate and complex potential are reconstructed by the Polubarinova-Kochina method, i.e., by solution of a Riemann BVP. The seepage flow rate from the channel, free surfaces, and a saturated (water-logged) area are found for different thicknesses of the top layer, channel widths, and conductivity ratios of the two strata. In particular, the earlier results of Brock, Kirkham, and Youngs, which are based on a numerical solution, Dupuit-Forchheimer (DF) approximation, and approximate potential model, are confirmed in the full 2-D models. Sufficiently far from the channel, the phreatic surface and interface make a wedge. For a sufficiently deep substratum, three zones are analytically distinguished: an almost vertical 1-D descending flow, an almost wedge-configured 1-D flow, and an essentially 2-D zone in between, where neither a standard infiltration theory nor DF analysis are valid.

AB - An analytical solution is obtained for steady 2-D potential seepage flow from a nonclogged and nonlined soil channel into a highly permeable porous layer, with phreatic surfaces tapering toward a horizontal interface with a subjacent low-permeable formation. Along this boundary, a vertical component of the Darcian velocity vector equals the formation saturated hydraulic conductivity. The image of the physical flow domain in the hodograph plane is a circular polygon, a triangle or digon in a limiting case of a "phreatic jet" impinging on the low-permeable substratum. The polygon is mapped onto an auxiliary half plane, where the complex physical coordinate and complex potential are reconstructed by the Polubarinova-Kochina method, i.e., by solution of a Riemann BVP. The seepage flow rate from the channel, free surfaces, and a saturated (water-logged) area are found for different thicknesses of the top layer, channel widths, and conductivity ratios of the two strata. In particular, the earlier results of Brock, Kirkham, and Youngs, which are based on a numerical solution, Dupuit-Forchheimer (DF) approximation, and approximate potential model, are confirmed in the full 2-D models. Sufficiently far from the channel, the phreatic surface and interface make a wedge. For a sufficiently deep substratum, three zones are analytically distinguished: an almost vertical 1-D descending flow, an almost wedge-configured 1-D flow, and an essentially 2-D zone in between, where neither a standard infiltration theory nor DF analysis are valid.

KW - conformal mappings

KW - hodograph

KW - infiltration

KW - managed aquifer recharge

KW - perched aquifer

KW - Polubarinova-Kochina method

UR - http://www.scopus.com/inward/record.url?scp=85027938670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027938670&partnerID=8YFLogxK

U2 - 10.1002/2014WR016304

DO - 10.1002/2014WR016304

M3 - Article

VL - 51

SP - 3093

EP - 3107

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 5

ER -