Steady Infiltration from Point Sources and Water Uptake in Confined Cylindrical Domains

Abstract

This article addresses the problem of steady water flow from point sources located in the center of a confined cylindrical domain. A linearized form of the water flow equation is used to analyze soil–water regimes, assuming exponential dependence of hydraulic conductivity on the matric head. Derived exact and approximate solutions are applicable to infiltration from a continuous point source into a cylindrical lysimeter and to water extraction by a subsurface point sink coupled to a surface source. Philip's superposition theorem, developed initially for a domain that is unconfined in the radial direction is shown to hold also for a cylindrically confined domain. An approximate, tractable expression keeping the first two terms of the full solution can satisfactorily replace the full accurate solution. Solutions for buried, surface, and subsurface point sources in a confined cylinder are expressed in terms of the dimensionless matric flux potential (MFP) and the dimensionless Stokes stream function. In the presence of an impermeable cylindrical boundary, the MFP decreases toward a constant value with increasing distance from the source, and the streamlines become more vertical at these distances. The smaller the cylinder radius or the soil sorptive number, the faster the MFP approaches constancy and the faster three‐dimensional flow converges to one‐dimensional flow below the source. Explicit expressions for the MFP and for the stream functions corresponding to a coupled surface point source and subsurface point sink in a semi‐infinite cylindrical domain are presented and used to simulate root water uptake rates in lysimeters. Water extraction rates produced by a coupled source/sink in the cylindrical domain are shown to be larger than those obtained in an unconfined domain and comparable with those computed for equivalent square‐arrays of coupled sources/sinks in open fields.