Steady infiltration flows with sloping boundaries

Abstract

General theorems are established that enable immediate solution of the quasilinear steady infiltration equation for any distribution of line and point sources at or beneath a sloping upper soil surface, or on or above a sloping impermeable base. The required solutions are readily deduced from the known simple solutions for buried line and point sources. Corollary to the theorems, similar relations hold for downslope and cross‐slope flux density components. Illustrative solutions are presented for line and point sources in the various configurations. Distributions of both potential and stream function are mapped for line sources and also for point sources at or beneath a horizontal surface. For other point sources, potential is mapped in the normal plane through the source. For sources beneath a surface, distortion due to the surface is relatively small, even for dimensionless normal source depth as small as 1. On the other hand, for sources above a sloping base, the base strongly skews the distributions of both potential and streamlines. Far downslope the flow is purely (line sources) or primarily (point sources) parallel to the base. Upper bounds exist on total source strength, beyond which a saturated region emerges, perched on a horizontal base. Consistent with earlier results and theorems, physically acceptable steady flows do not exist above the base.