### Abstract

Steady, two-dimensional Darcian flow in a homogeneous isotropic unconfined aquifer, bounded from below by a rectangular wedge representing bedrock, is studied by the theory of holomorphic functions. A triangle of the complex potential domain is mapped onto a circular triangle in the hodograph plane with the help of an auxiliary variable. A full potential theory results in closed-form integral representations for the complex potential and complex velocity, from which the flow rate and free surface are calculated using computer algebra built-in functions. This solution, uniformly valid in the whole flow domain, is compared with simpler approximate ones, retrieved from an analytical archive. Two flow zones are distinguished: a tranquil subdomain where the Dupuit-Forchheimer approximation is suitable and a nappe (a subdomain with a rapidly changing Darcian velocity and steep slope of the phreatic surface) where the Numerov or Polubarinova-Kochina solutions, in terms of the full potential model, are available. Approximations in the two zones are conjugated by matching the positions of the water table and the flow rates, which eventually agree well with the obtained comprehensive solution.

Original language | French |
---|---|

Pages (from-to) | 1203-1209 |

Number of pages | 7 |

Journal | Hydrogeology Journal |

Volume | 20 |

Issue number | 6 |

DOIs | |

Publication status | Published - Sep 2012 |

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### Keywords

- Complex potential
- Dupuit-Forchheimer approximation
- Groundwater flow
- Hodograph
- Phreatic surface

### ASJC Scopus subject areas

- Earth and Planetary Sciences (miscellaneous)
- Water Science and Technology

### Cite this

**Solution analytique pour un abaissement du niveau piézométrique : Les solutions de Riesenkampf et Numerov revisitées.** / Kacimov, A. R.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Solution analytique pour un abaissement du niveau piézométrique

T2 - Les solutions de Riesenkampf et Numerov revisitées

AU - Kacimov, A. R.

PY - 2012/9

Y1 - 2012/9

N2 - Steady, two-dimensional Darcian flow in a homogeneous isotropic unconfined aquifer, bounded from below by a rectangular wedge representing bedrock, is studied by the theory of holomorphic functions. A triangle of the complex potential domain is mapped onto a circular triangle in the hodograph plane with the help of an auxiliary variable. A full potential theory results in closed-form integral representations for the complex potential and complex velocity, from which the flow rate and free surface are calculated using computer algebra built-in functions. This solution, uniformly valid in the whole flow domain, is compared with simpler approximate ones, retrieved from an analytical archive. Two flow zones are distinguished: a tranquil subdomain where the Dupuit-Forchheimer approximation is suitable and a nappe (a subdomain with a rapidly changing Darcian velocity and steep slope of the phreatic surface) where the Numerov or Polubarinova-Kochina solutions, in terms of the full potential model, are available. Approximations in the two zones are conjugated by matching the positions of the water table and the flow rates, which eventually agree well with the obtained comprehensive solution.

AB - Steady, two-dimensional Darcian flow in a homogeneous isotropic unconfined aquifer, bounded from below by a rectangular wedge representing bedrock, is studied by the theory of holomorphic functions. A triangle of the complex potential domain is mapped onto a circular triangle in the hodograph plane with the help of an auxiliary variable. A full potential theory results in closed-form integral representations for the complex potential and complex velocity, from which the flow rate and free surface are calculated using computer algebra built-in functions. This solution, uniformly valid in the whole flow domain, is compared with simpler approximate ones, retrieved from an analytical archive. Two flow zones are distinguished: a tranquil subdomain where the Dupuit-Forchheimer approximation is suitable and a nappe (a subdomain with a rapidly changing Darcian velocity and steep slope of the phreatic surface) where the Numerov or Polubarinova-Kochina solutions, in terms of the full potential model, are available. Approximations in the two zones are conjugated by matching the positions of the water table and the flow rates, which eventually agree well with the obtained comprehensive solution.

KW - Complex potential

KW - Dupuit-Forchheimer approximation

KW - Groundwater flow

KW - Hodograph

KW - Phreatic surface

UR - http://www.scopus.com/inward/record.url?scp=84866093046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866093046&partnerID=8YFLogxK

U2 - 10.1007/s10040-012-0857-z

DO - 10.1007/s10040-012-0857-z

M3 - Article

VL - 20

SP - 1203

EP - 1209

JO - Hydrogeology Journal

JF - Hydrogeology Journal

SN - 1431-2174

IS - 6

ER -