An Analytical Model of Chaotic Advection in Regional Groundwater Flow Driven by Periodic Water Table Fluctuations and Depth-Dependent Aquifer Properties

Accurate prediction of groundwater flow dynamics is often limited by the assumption of spatially uniform aquifer properties, which can result in biased hydraulic head estimates. Although the depth dependence of aquifer parameters is well recognized, most available analytical solutions remain confined to homogeneous aquifer systems. This study presents a two-dimensional transient analytical model for a regional single-layer aquifer subjected to a fluctuating water table, explicitly incorporating depth-dependent hydraulic conductivity and specific storage, along with pumping effects. The analytical solution is obtained using the Generalized Integral Transform Technique (GITT), which implicitly enforces continuity of hydraulic head and flux across depth variations without the need for iterative eigenvalue estimation, thereby providing a robust framework for representing stratified aquifer behavior. Model verification is conducted using a benchmark single-layer solution, and independent validation is performed through COMSOL Multiphysics simulations, demonstrating excellent agreement. The influence and reliability of model parameters are further evaluated using global sensitivity analysis. A key novel contribution of this work is the identification of chaotic flow behavior within a single-layer Tóthian basin, examined using the Finite-Time Lyapunov Exponent (FTLE). The results reveal that chaotic dynamics are most pronounced near the upper boundary, where FTLE values are significantly higher than in deeper regions, with further intensification observed under periodic injection in a single-well system. Overall, the proposed analytical framework addresses a critical gap in transient single-layer groundwater flow modeling, enhances the theoretical understanding of stratified aquifer systems, and provides a reliable benchmark for numerical simulations and field-scale groundwater studies.