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.