Abstract
Groundwater level in coastal aquifers is usually affected by tidal waves and rainfall recharge. Therefore, the objective of this study is to present a mathematical model to account for the effects of tidal waves and rainfall recharge simultaneously. The model is based on the Dupuit–Forchheimer assumptions and is separated into a tidal waves component and rainfall recharge component. A new more general analytical solution for the recharge component is acquired by the generalized integral transform technique. The beach slope, the inclination of an impermeable base of an aquifer, and any randomly distributed rainfall recharge are taken into account in the model. A new finding is that the highest fluctuation in groundwater levels might occur when the range of rainfall recharge is larger than the decay length.
Highlights
The estimation of groundwater levels is usually simulated by numerical models in addition to field observations of wells
Nielsen et al [3] investigated the variation of the beach slopes of coastal aquifers and derived analytical solutions for groundwater tables inside horizontal aquifers
The present solutions which consider the moving boundary are more general than the previous present solutions which consider the moving boundary are more general than the previous solutions solutions of et Parlange et al
Summary
The estimation of groundwater levels is usually simulated by numerical models in addition to field observations of wells. Parlange et al [1] applied the theory proposed by Dagan [2] to analytically investigate tidal waves’ effect on the groundwater level fluctuations in spatial and temporal variations. Their results agree very well with that obtained by numerical models but are only restricted to vertical beach slopes. In their study, the shoreline, i.e., the free water surface at the interface between the aquifer and ocean water, is considered to be fixed This is not true for real physical phenomena. Li et al [4] proposed a moving boundary method to modify the shortcomings of the fixed boundary concept for an inclined beach
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