Stagnation and Pseudo-Stagnation Lines for Separating 3D Groundwater Flow Systems in Tóthian Basins

Stagnation points have been found to be useful in characterizing groundwater flow regimes in 2D domains. However, knowledge on stagnation points in 3D basins is limited. In this study, we first derive a transient solution for 3D Tóthian basin flow under spatially undulating and periodically changing water table and examine the occurrence of stagnation points or pseudo-stagnation points, which constitute stagnation lines or pseudo-stagnation lines in the 3D domain. Then, we propose a method of delineating 3D groundwater flow systems using stagnation or pseudo-stagnation lines for the first time, and successfully apply it to 3D synthetic basins with either steady-state or transient groundwater flow. In 3D basins with periodically fluctuating water tables, transient stagnation or pseudo-stagnation lines are controlled by the combination of hydraulic diffusivity and the period of water table fluctuation, both of which determine the dimensionless response time, and their variations reflect the evolution of transient groundwater flow systems and control the tortuosity of particle trajectories. This study enhances the efficiency of dividing groundwater flow systems in 3D basins and also improves the knowledge on how stagnation or pseudo-stagnation points influence streamlines and trajectories.