### Abstract

Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.

Original language | English (US) |
---|---|

Pages (from-to) | 793-800 |

Number of pages | 8 |

Journal | Water Resources Research |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Aquatic Science
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology

### Cite this

*Water Resources Research*,

*36*(3), 793-800. https://doi.org/10.1029/1999WR900317

**Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer.** / Verhoest, Niko E C; Troch, Peter A.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 36, no. 3, pp. 793-800. https://doi.org/10.1029/1999WR900317

}

TY - JOUR

T1 - Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer

AU - Verhoest, Niko E C

AU - Troch, Peter A

PY - 2000

Y1 - 2000

N2 - Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.

AB - Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.

UR - http://www.scopus.com/inward/record.url?scp=0034064692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034064692&partnerID=8YFLogxK

U2 - 10.1029/1999WR900317

DO - 10.1029/1999WR900317

M3 - Article

AN - SCOPUS:0034064692

VL - 36

SP - 793

EP - 800

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 3

ER -