Groundwater dynamics due to general stream fluctuations in an unconfined single or dual-porosity aquifer subjected to general areal recharge

Analytical solutions of groundwater dynamics in an elongated aquifer subjected to general time-dependent recharge are presented. The lateral boundaries are specified heads with the head variations governed by general time-dependent functions. General recharge function was not considered in previous works of this kind. Both single and double-porosity aquifers are considered. The solution is obtained using Fourier sine and Laplace transformations, followed by an inverse Fourier-Laplace transform involving residue theorem and convolutional integral. For the unconfined single-porosity aquifer case, the exact time-domain solution is obtained using the residue theorem; for the unconfined double-porosity aquifer case, the time-domain head is calculated using the de Hoog inverse Laplace algorithm. The presented solution can be used to estimate the hydraulic parameters of 1) groundwater head variation of a river basin aquifer subjected to general lateral head variation and recharge; 2) groundwater head variation in a double-porosity elongated fractured anticline; 3) groundwater depletion of an elongated fractured anticline subjected to recharge due to rainfall or snowmelt to its adjacent alluvial aquifer. In addition, the presented solution can be utilized to optimize the irrigation pattern in a cropland between two trench drains to control the groundwater mound.