Analytical solutions for strip basin recharge to aquifers with Cauchy boundary conditions

Latinopoulos, P.

doi:10.1016/0022-1694(86)90151-4

Cited by 15 publications

(20 citation statements)

References 13 publications

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“…Previous articles have discussed groundwater mounds in response to localized recharge into aquifers with various hydraulic parameters (e.g., Dagan, 1967;Rao and Sarma, 1980;Latinopoulos, 1986;Manglik et al, 1997;Manglik and Rai, 1998;Rai et al, 1998;Chang and Yeh, 2007;Illas et al, 2008;Bansal and Das, 2010;Bansal and Teloglou, 2013). Flow velocity fields below groundwater mounds have also been analyzed Ledder, 1992, 1993).…”

Section: Resultsmentioning

confidence: 99%

“…Later, they developed a solution (Rao and Sarma, 1984) for a finite-extent aquifer between no-flow and constant-head boundaries. Latinopoulos (1986) deliberated on a finite-extent aquifer between two boundaries, one of which is under the Robin condition and the other is under either the Dirichlet or no-flow condition. The recharge rate is treated as a periodical pulse consisting of constant rates for rainy seasons and zero for dry seasons.…”

Section: Introductionmentioning

confidence: 99%

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Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Chang

Huang

Yeh

2016

Hydrol. Earth Syst. Sci.

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Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table movement. The solution to the model for the head is developed with the methods of Laplace transform and double-integral transform. Based on Duhamel's theorem, the present solution is applicable to flow problems accounting for arbitrary time-dependent recharge rates. The solution to depth-average head can then be obtained by integrating the head solution to elevation and dividing the result by the aquifer thickness. The use of a rectangular aquifer domain has two merits. One is that the integration for estimating the depth-average head can be analytically achieved. The other is that existing solutions based on aquifers of infinite extent can be considered as special cases of the present solution before the time when the aquifer boundary had an effect on head predictions. With the help of the present solution, the assumption of neglecting the vertical flow effect on the temporal head distribution at an observation point outside a recharge region can be assessed by a dimensionless parameter related to the aquifer horizontal and vertical hydraulic conductivities, initial aquifer thickness, and the shortest distance between the observation point and the edge of the recharge region. The validity of assuming aquifer incompressibility is dominated by the ratio of the aquifer specific yield to its storage coefficient. In addition, a sensitivity analysis is performed to investigate the head response to the change in each of the aquifer parameters.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Chang

Huang

Yeh

2016

Hydrol. Earth Syst. Sci.

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“…For the transient flow problem depicted in Figure , some analytical or semianalytical solutions are provided in the literature: The case of transient two‐dimensional (2‐D) horizontal flow in an unconfined aquifer was investigated by Latinopoulos []; the linearized Boussinesq equation subject to Robin BCs was solved by Laplace and finite Fourier transforms. The interactions of a clogged stream with confined, leaky, and water table aquifers were considered by Moench and Barlow []; for the last case, 2‐D flow in a plane perpendicular to the stream was considered.…”

Section: Introductionmentioning

confidence: 99%

Solutions of the Boussinesq equation subject to a nonlinear Robin boundary condition

Μουτσόπουλος

2013

Water Resources Research

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[1] The case of inflow to an aquifer or porous medium inhibited by the presence of a semipervious (clogging) layer is investigated. The flow process is characterized by transient, free surface flow conditions. Here, unlike in previous studies, the nonlinear Boussinesq equation is considered. The influence of the clogging layer is simulated by imposing a nonlinear Robin (third kind) boundary condition at the edge of the aquifer. A semianalytical solution was derived by using the Adomian decomposition method, whose validity was checked by solving the problem by a finite difference method. By adopting a nondimensional analysis, the hydraulic behavior of the investigated problem was presented also in tabular form. Potential application examples are the study of water body-aquifer interactions and the hydraulic processes inside a permeable dam with a semipervious core.

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“…Mathematical models play a key role in assessing future behaviour of a groundwater system in response to various operational schemes of recharging and in the selection of an appropriate scheme out of the many proposed for sustainable development of groundwater resources. Many workers have derived analytical solutions to predict the water table fluctuations in response to recharge from a strip basin (Marino, 1967(Marino, , 1974Rao and Sarma, 1983;Latinopoulos, 1986). Most of these solutions are based on the assumption of constant rate of recharge applied continuously or periodically.…”

Section: Introductionmentioning

confidence: 99%

Modelling of groundwater mound formation resulting from transient recharge

Ramana

Thiagarajan

et al. 2001

Hydrological Processes

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Abstract:An analytical solution of a linearized Boussinesq equation is obtained to predict water table fluctuations as a result of time varying recharge from a strip basin for any number of recharge cycles. The analytical solution is obtained by using finite Fourier sine transform. Applications of the solution for the prediction of water table fluctuations and sensitivity analysis are demonstrated with the help of example problems.

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Analytical solutions for strip basin recharge to aquifers with Cauchy boundary conditions

Cited by 15 publications

References 13 publications

Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Solutions of the Boussinesq equation subject to a nonlinear Robin boundary condition

Modelling of groundwater mound formation resulting from transient recharge

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