Beach water table fluctuations due to spring–neap tides: moving boundary effects

Li, Ling; Barry, David Andrew; Stagnitti, Frank; Parlange, J.‐Y.; Jeng, Dong‐Sheng

doi:10.1016/s0309-1708(00)00017-8

Cited by 178 publications

(166 citation statements)

References 7 publications

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“…This means that in the present paper, Vt should always be no larger than h i . Similar to Li et al (2000), we introduce a new variable z ¼ x À XðtÞ, indicating the horizontal distance between a point in the aquifer and the intersection of reservoir water-surface level and sloped interface. Eqs.…”

Section: Governing Equation For Transient Groundwater Flows With a Momentioning

confidence: 99%

“…He derived a perturbation solution for small-amplitude fluctuations in the water table on the basis of the linearized Boussinesq equation by matching a prescribed series solution with the moving boundary condition. Li et al (2000) transformed the Boussinesq equation into an advection-diffusion equation with an oscillating water table to account for the moving boundary effect. Maintaining the simplicity of the linearized Boussinesq equation, they presented a new perturbation approach to deal with the propagation of spring neap tides.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of the present paper is to extend the work of Li et al (2000) to determine the groundwater table location during reservoir drawdown. A new analytical solution of the linearized Boussinesq equation is presented to describe groundwater table variation in a semi-infinite unconfined aquifer when reservoir water drops at a constant speed.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Engineering Solution for Predicting Groundwater Table Variation During Reservoir Drawdown on the Basis of the Boussinesq Equation

Sun

Liu

et al. 2011

J. Hydrol. Eng.

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With reservoir drawdown, the groundwater table in the adjacent aquifer falls down correspondingly. It is useful to calculate the groundwater table variation as a function of time during reservoir drawdown for hydraulic and hydrological purposes. The Boussinesq equation with a moving boundary is applied to analyze the groundwater table variation in the unconfined aquifer during reservoir drawdown. This approach assumes a negligible seepage face. Because the moving boundary condition in the mathematical formulation precludes analytical solutions even for the linearized Boussinesq equation, we have transformed the Boussinesq equation into an advection-diffusion equation to address the negligible seepage face and the moving boundary condition. On the basis of the Laplace transformation, we yield an analytical solution of a fixed boundary problem, which is further simplified to upper and lower polynomial solutions for convenient practical use. The polynomial approximate solutions are satisfactorily compared with a number of numerical simulations of the nonlinear Boussinesq equation. The results indicate that the polynomial solutions match well with the numerical solution, but demonstrate that the replacement of the sloped reservoir-aquifer interface by a vertical interface may cause errors of up to 10% of the height of the reservoir drawdown in the prediction of the groundwater table location. On the basis of the polynomial solutions, a methodology is provided to determine the ratio of hydraulic conductivity to specific yield along with a chart for convenient practical use. The limitation of the present study is that the presented solution tends to underestimate the groundwater table with seepage face neglected for rapid drawdown, high specific yield, low hydraulic conductivity, or mildly sloped interface cases.

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Section: Governing Equation For Transient Groundwater Flows With a Momentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximate Engineering Solution for Predicting Groundwater Table Variation During Reservoir Drawdown on the Basis of the Boussinesq Equation

Sun

Liu

et al. 2011

J. Hydrol. Eng.

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“…Since then, many scholars have reached the same conclusion as Ataie-Ashtiani's. They also believed that the effect of tidal action on brackish water interface is small, and the geomorphology and stratigraphic features of sea beach are also important factors in affecting the coastal groundwater [5] [6] [7] [8]. However, all the studies were based on mathematical analysis and numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Effect of Tides on the Stratigraphic Resistance of the South Coast of the Laizhou Bay

Su¹,

Xu²,

Liu³

et al. 2017

JWARP

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Seawater intrusion is a global environmental problem that is becoming increasingly severe with the overexploitation of underground freshwater in coastal regions and sea-level rise caused by global climate change. Although a series of achievements has been made on seawater intrusion, the role of tidal effects has not been fully revealed. In this paper, a typical case of tidal effects on seawater intrusion is provided. The high-density resistivity method was applied to the high-frequency continuous measurement of the stratigraphic resistance of the south coast of the Laizhou Bay, followed by the panel data analysis method. The results indicate that the formation resistivity in coastal area was affected by the tidal level significantly, particularly in the seawater intrusion channel. The effect of tide on the intensity distribution of formation resistivity was evaluated using this method. Because of the presence of a brine layer in the section, the trends of the tidal level effect on the formation resistivity in the left and right sides of the section were opposite, and the intensity of the effect increased sideways.

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“…For more realistic case of beach slopes, Nielsen (1990) considered a movable shoreline boundary condition and derived an analytical solution for groundwater fluctuations in costal aquifers with a sloping beach. Li et al (2000) further overcame the inconsistency of the boundary condition in Nielsen's solution and utilized the same parameter in Nielsen (1990) to develop a solution for the problem using a concept of moving boundary. Since the slope of the beach was included in the perturbation parameter in both models, their models may be applicable to a certain range of the beach slopes.…”

Section: Introductionmentioning

confidence: 99%

Tidal propagation in an oceanic island with sloping beaches

Chang

Jeng

Yeh

2010

Hydrol. Earth Syst. Sci.

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Abstract. In this study, a new analytical solution for describing the tide-induced groundwater fluctuations in oceanic islands with finite length and different slopes of the beaches is developed. Unlike previous solutions, the present solution is not only applicable for a semi-infinite coastal aquifer, but also for an oceanic island with finite length and different sloping beaches. The solution can be used to investigate the effect of higher-order components and beach slopes on the water table fluctuations. The results demonstrate the effect of higher-order components increases with the shallow water parameter or amplitude parameter and the water table level increases as beach slopes decrease.

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Beach water table fluctuations due to spring–neap tides: moving boundary effects

Cited by 178 publications

References 7 publications

Approximate Engineering Solution for Predicting Groundwater Table Variation During Reservoir Drawdown on the Basis of the Boussinesq Equation

Approximate Engineering Solution for Predicting Groundwater Table Variation During Reservoir Drawdown on the Basis of the Boussinesq Equation

Effect of Tides on the Stratigraphic Resistance of the South Coast of the Laizhou Bay

Tidal propagation in an oceanic island with sloping beaches

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