Steady recharge-induced groundwater flow over a plane bed: nonlinear and linear solutions

Abstract: The form of the free surface in two-dimensional groundwater flow over a plane impermeable bed, induced by percolating rainfall or irrigation, has been the subject of considerable study since the 1960's. The earlier analyses were related to drainage design, but more recently, and particularly for the case of a sloping bed, the motivation has been the development of models of hillslope hydrology, and there has been particular interest in linearisation of the Boussinesq equation. This paper first develops a quasi-analytical solution for the maximum water-table height in the case of a horizontal bed, and compares this with the Boussinesq and linearised Boussinesq solutions. In the case of a sloping bed, it is shown that the Boussinesq equation can be reduced to a single dimensionless form, dependent on the system of coordinates and the direction of the recharge. Numerical solutions are given for the steady flow case, indicating the conditions under which the linearised solutions depart markedly from the Boussinesq equation