ANALYTIC SOLUTIONS FOR UNCONFINED GROUNDWATER-FLOW OVER A STEPPED BASE

Two new exact solutions are presented for uniform unconfined groundwat er flow over a stepped base; one for a step down in the direction of f low, the other for a step up in the direction of flow. These are two-d imensional solutions of Laplace's equation in the vertical plane, and are derived using the hodograph method and conformal mappings on Riema nn surfaces. The exact solutions are compared with approximate one-dim ensional solutions which neglect the resistance to vertical flow. For small horizontal hydraulic gradients typical of regional groundwater f low, little error is introduced by neglecting the vertical resistance to flow. This conclusion may be extended to two-dimensional analytical models in the horizontal plane, which neglect the vertical resistance to flow and treat the aquifer base as a series of flat steps.