TY - JOUR

T1 - Rainfall induced groundwater mound in wedge-shaped promontories: The Strack-Chernyshov model revisited

T2 - The Strack–Chernyshov model revisited

AU - Kacimov, A. R.

AU - Kayumov, I. R.

AU - Al-Maktoumi, A.

N1 - Publisher Copyright:
© 2016 Elsevier Ltd

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 - Dirichlet conditions for Poisson equation

KW - Analytic and numeric solutions

KW - Dupuit-Forchheimer model

KW - Water table with natural recharge

KW - Evaporation and sea water intrusion

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U2 - 10.1016/j.advwatres.2016.08.011

DO - 10.1016/j.advwatres.2016.08.011

M3 - Article

AN - SCOPUS:84988009617

SN - 0309-1708

VL - 97

SP - 110

EP - 119

JO - Advances in Water Resources

JF - Advances in Water Resources

ER -