Transport in Porous Media 27: 121–134, 1997. 121 c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Perturbation Analysis for Wetting Fronts in Richards’ Equation THOMAS P. WITELSKI Department of Mathematics, 2-336 Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. e-mail: witelski@math.mit.edu (Received: 1 March 1996; in final form: 20 December 1996) Abstract. Perturbation methods are used to study the interaction of wetting fronts with impervious boundaries in layered soils. Solutions of Richards’ equation for horizontal and vertical infiltration problems are considered. Asymptotically accurate solutions are constructed from outer solutions and boundary-layer corrections. Results are compared with numerical simulations to demonstrate a high level of accuracy. Key words: Richards’ equation, nonlinear diffusion, infiltration, layered soils, wetting fronts, pertur- bation methods 1. Introduction We study the motion of wetting fronts for infiltration problems in layers of initially dry soil. Our focus is the analysis of how propagating wetting fronts interact with fixed impervious layers. Using perturbation methods, we will make precise the ‘short-term superposition principle’ for the interaction of diffusive profiles with stratification boundaries suggested by Parlange (Parlange et al., 1994a, b; Hogarth et al., 1995). For studies of horizontal and vertical infiltration of groundwater, this analysis can be used to estimate how quickly moisture collects at an impervious boundary in the soil. We show how the technique of matched asymptotic expan- sions (Kevorkian and Cole, 1981) allows analytic or semi-analytic solutions of Richards’ equation to be appropriately combined to yield the behavior for moisture content in layered soils. Following a brief review of classical infiltration results for Richards’ equation, we examine a boundary value problem for horizontal and vertical infiltration with an impervious boundary. Transport of groundwater in unsaturated porous media is governed by the con- servation law q 0 q (1) where x is the local volumetric moisture content, and the flux is given by Dar- cy’s law (Bear, 1972), where is the soil conductivity and is the moisture potential (or pressure head). For essentially unidirectional one-dimensional flows,