scholarly journals Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 826 ◽  
Author(s):  
Wu ◽  
Hsieh
Keyword(s):  
Groundwater Level ◽  
Boussinesq Equation ◽  
Integral Transformation ◽  
Transformation Method ◽  
Unconfined Aquifer ◽  
Convergence Criterion ◽  
Unconfined Aquifers ◽  
Linearized Boussinesq Equation ◽  
Sloping Aquifer ◽  
Rainfall Recharge

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.

scholarly journals Variation of Groundwater Flow Caused by Any Spatiotemporally Varied Recharge

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 287
Author(s):  
Ming-Chang Wu ◽  
Ping-Cheng Hsieh
Keyword(s):  
Analytical Solution ◽  
Groundwater Flow ◽  
Unconfined Aquifer ◽  
Initial Water ◽  
The Past ◽  
Sloping Aquifer ◽  
Taichung City ◽  
Spatially Distributed ◽  
Recharge Rates ◽  
Rainfall Recharge

The objective of this study was to develop a complete analytical solution to determining the effect of any varying rainfall recharge rates on groundwater flow in an unconfined sloping aquifer. The domain of the unconfined aquifer was assumed to be semi-infinite with an impervious bottom base, and the initial water level was parallel to the impervious bottom of a mild slope. In the past, similar problems have been discussed mostly by considering a uniform or temporally varying recharge rate, but the current study explored the variation of groundwater flow under temporally and spatially distributed recharge rates. The presented analytical solution was verified by comparing its results with those of previous research, and the practicability of the analytical solution was validated using the 2012 and 2013 data of a groundwater station in Dali District of Taichung City, Taiwan.

scholarly journals Underground Barrier Wall Evaluation for Controlling Saltwater Intrusion in Sloping Unconfined Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2403
Author(s):  
Asaad M. Armanuos ◽  
Nadhir Al-Ansari ◽  
Zaher Mundher Yaseen
Keyword(s):  
Saltwater Intrusion ◽  
Cost Benefit Analysis ◽  
Cost Benefit ◽  
Unconfined Aquifer ◽  
Numerical Results ◽  
Unconfined Aquifers ◽  
Sloping Bed ◽  
Bed Slope ◽  
The Cost ◽  
Barrier Wall

Barrier walls are considered one of the most effective methods for facilitating the retreat of saltwater intrusion (SWI). This research plans to examine the effect of using barrier walls for controlling of SWI in sloped unconfined aquifers. The sloping unconfined aquifer is considered with three different bed slopes. The SEAWAT model is implemented to simulate the SWI. For model validation, the numerical results of the seawater wedge at steady state were compared with the analytical solution. Increasing the ratio of flow barrier depth (db/d) forced the saltwater interface to move seaward and increased the repulsion ratio (R). With a positive sloping bed, further embedding the barrier wall from 0.2 to 0.7 caused R to increase from 0.3% to 59%, while it increased from 1.8% to 41.7% and from 3.4% to 46.9% in the case of negative and horizontal slopes, respectively. Embedding the barrier wall to a db/d value of more than 0.4 achieved a greater R value in the three bed-sloping cases. Installing the barrier wall near the saltwater side with greater depth contributed to the retreat of the SWI. With a negative bed slope, moving the barrier wall from Xb/Lo = 1.0 toward the saltwater side (Xb/Lo = 0.2) increased R from 7.21% to 68.75%, whereas R increased from 5.3% to 67% for the horizontal sloping bed and from 5.1% to 64% for the positive sloping bed. The numerical results for the Akrotiri coastal aquifer confirm that the embedment of the barrier wall significantly affects the controlling of SWI by increasing the repulsion ratio (R) and decreasing the SWI length ratio (L/La). Cost-benefit analysis is recommended to determine the optimal design of barrier walls for increasing the cost-effectiveness of the application of barrier walls as a countermeasure for controlling and preventing SWI in sloped unconfined aquifers.

scholarly journals Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

2020 ◽  
Vol 11 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Groundwater Flow ◽  
Governing Equation ◽  
Water Flux ◽  
Unconfined Aquifer ◽  
Saturated Porous Media ◽  
Unconfined Aquifers ◽  
Heavy Tailed ◽  
Consistent Equation ◽  
Fractional Dimensions ◽  
Fractional Space

Abstract. In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.

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