Stagnation lines and its control of nested groundwater flow systems in three-dimensional Tóthian basins

The theory of groundwater flow systems proposed by Tóth, which was based on the two-dimensional profile flow field, has become the theoretical basis for studying basin-scale groundwater circulation.The stagnation points on the two-dimensional profile can be used to accurately divide the spatial distribution of groundwater flow systems.However, the spatial distribution of groundwater flow systems and whether stagnation points exist in the 3D domain remain unknown.In this study, two typical three-dimensional basins, namely foreland-like basins with undulations only in the x direction and dune-type basins with undulations in both x and y directions, are used as typical examples.By using a combination of cosine functions to characterize the undulating water table, analytical solutions of head distribution in the two basins are derived.Moreover, by employing the TECPLOT software, the spatial distribution of the 3D groundwater flow systems is clearly shown.It is found out that stagnation points can develop in two basins.The stagnation points in the foreland-like basin constitute a horizontally extending stagnation line, which controls the spatial distribution of four flow systems in the basin, while the stagnation points in the dune-type basin form an arc-shaped stagnation line, which controls the spatial distribution of six flow systems in the basin.By studying the distribution of stagnation line in 3D basins and successfully dividing flow systems by using the stagnation line, this study leads to a deepened understanding of groundwater circulation in 3D basins.