### Abstract

An analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential.

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

Pages (from-to) | 110-119 |

Number of pages | 10 |

Journal | Advances in Water Resources |

Volume | 97 |

DOIs | |

Publication status | Published - Nov 1 2016 |

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### Keywords

- Analytic and numeric solutions
- Dirichlet conditions for Poisson equation
- Dupuit–Forchheimer model
- Evaporation and sea water intrusion
- Water table with natural recharge

### ASJC Scopus subject areas

- Water Science and Technology

### Cite this

**Rainfall induced groundwater mound in wedge-shaped promontories : The Strack–Chernyshov model revisited.** / Kacimov, A. R.; Kayumov, I. R.; Al-Maktoumi, A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Rainfall induced groundwater mound in wedge-shaped promontories

T2 - The Strack–Chernyshov model revisited

AU - Kacimov, A. R.

AU - Kayumov, I. R.

AU - Al-Maktoumi, A.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - An analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential.

AB - An analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential.

KW - Analytic and numeric solutions

KW - Dirichlet conditions for Poisson equation

KW - Dupuit–Forchheimer model

KW - Evaporation and sea water intrusion

KW - Water table with natural recharge

UR - http://www.scopus.com/inward/record.url?scp=84988009617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988009617&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2016.08.011

DO - 10.1016/j.advwatres.2016.08.011

M3 - Article

AN - SCOPUS:84988009617

VL - 97

SP - 110

EP - 119

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

ER -