Recharge-induced groundwater flow over a plane sloping bed: Solutions for steady and transient flow using physical and numerical models

The free surface profile and outflow hydrograph for groundwater under conditions of steady uniform recharge followed by recession have been studied in viscous fluid model tests, using a sloping bed with a gradient of 0.2. The data have been compared with the nonlinear Boussinesq model and a modification of that model simulating the outflow seepage surface, obtained from a finite difference solution of the free boundary problem. It is shown that for a given bed slope, there is close to a linear relationship between outflow and storage raised to a power n, where n ranges from almost 2 for zero slopes to just above 1 at a gradient of 0.3. There is also a simple relationship between outflow and storage in the final stage of recession, when a drainage front occurs on the bed. These results lead to simple algorithms for prediction of the outflow under unsteady recharge conditions.