A new analytical solution of topography‐driven flow in a drainage basin with depth‐dependent anisotropy of permeability

Theoretical analysis and field observations suggest that the depth‐dependent trend of permeability anisotropy is a nature of the geological media accompanying the depth‐decaying permeability. However, the effect of depth‐dependent anisotropy has not been investigated in previous studies of regional groundwater flow. A more general analytical solution of topography‐driven flow in drainage basins is derived in this study. Exponential trend of permeability with depth is assumed, and different decay rates of horizontal permeability ( k x ) and vertical permeability ( k z ) are included to account for the depth‐dependent anisotropy. It is found that the shape of the nested flow systems in a drainage basin depends on not only the depth‐dependent permeability but also the depth‐dependent anisotropy ratio ( k x / k z ). For stagnation points between the flow systems, the number of stagnation points is not influenced by the depth‐dependent permeability and anisotropy; however, an increase in k x / k z can lead to a decrease in the depth of their location. When k x is smaller than k z on the top boundary, this phenomenon is especially significant.