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An Analytical Solution of Groundwater Flow in Wedge-shaped Aquifers with Estuarine Boundary Conditions

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Abstract

The issue of the groundwater fluctuation due to tidal effect in a two-dimensional coastal leaky aquifer system has attracted much attention in recent years. The predictions of head fluctuation play an important role in dealing with groundwater managements and contaminant remediation problems in costal aquifers. This article presents a two-dimensional analytical model describing the groundwater flow in a coastal leaky aquifer of wedge shape affected by the tides and bounded by two estuarine rivers with an arbitrary included angle. The solution of the model is derived in the Polar coordinates by the Hankel transform and finite sine transform. The head fluctuation predicted by this new solution is compared with that by an existing solution for groundwater flow in a non-L shaped tidal aquifer. The groundwater fluctuation due to the joint effect of estuarine tides is explored based on the present solution. Moreover, the influences of the parameters such as diffusion (Di), included angle (Ф), and tidal river coefficients (K1, K2) on the head fluctuation in the aquifer are also assessed and discussed. The results demonstrate that those parameters have significant effects on the head fluctuation in the leaky confined aquifer system. Moreover, the effect of Di increases with Ф, and the effects of K1 and K2 on the normalized amplitude and phase lag of the groundwater fluctuation are significant when both parameter values are larger than 10−5.

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Abbreviations

A, A 1 , A 2 :

Amplitudes of the tidal change [L]

c, c 1 , c 2 :

Phase shifts of the tidal change [rad]

D i :

Diffusion [L2 T−1]

f* :

Hankel transform

h(r, θ, t):

Hydraulic head [L]

\( \overline{h}\left(r,\theta \right) \) :

Hydraulic head [L]

h A :

Normalized amplitude of head fluctuation

h m :

Hydraulic head from the datum [L]

i :

\( \sqrt{-1} \)

TID:

Tidal intrusion distance

\( {J}_{\mu_n}\left(\cdot \right) \) :

Bessel function of the first kind of order μn

K 1, K 2 :

Tidal river coefficients

K 1r, K 2r :

Damping coefficients of tidal amplitude

K 1i, K 2i :

Separation coefficients

L :

Leakage [T−1]

n :

Positive integer series

ph :

Phase lag

r :

Distance for Polar coordinate [L]

S :

Storage coefficient

S i :

Coefficient given by Eq. 4

T :

Transmissivity [L2 T−1]

t :

Time [T]

t 0 :

Tidal period [T]

u :

Dumb variable for Hankel transform

u c , u k1 , u k2 :

Coefficients defined by Eq. 8

ω,ω 1,ω 2 :

Tidal speeds [rad/T]

θ :

Angle for Polar coordinate [rad]

Ф :

Angle for two boundaries [rad]

μ n :

Order of Bessel function of the first kind

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Acknowledgements

This study was supported by the Taiwan Ministry of Science and Technology under the grant MOST 107-2221-E-009-019-MY3 and 106-2621-M-130-002-.

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Authors and Affiliations

  1. Department of Urban Planning and Disaster Management, Ming-Chuan University, Taoyuan, Taiwan

    Mo-Hsiung Chuang

  2. Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan

    Hund-Der Yeh

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  1. Mo-Hsiung Chuang
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  2. Hund-Der Yeh
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Correspondence to Hund-Der Yeh.

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Chuang, MH., Yeh, HD. An Analytical Solution of Groundwater Flow in Wedge-shaped Aquifers with Estuarine Boundary Conditions. Water Resour Manage 32, 5027–5039 (2018). https://doi.org/10.1007/s11269-018-2125-z

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  • DOI: https://doi.org/10.1007/s11269-018-2125-z

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