Scattering Functions and Infiltration

In the theory of the scattering of plane harmonic waves by an obstacle Van de Hulst theorems give simple connections between the forward scattering function and the total extinction cross section. In this paper analogous theorems are proved for two‐ and three‐dimensional quasi‐linear steady flows in saturated soils from finite cavities of arbitrary size and shape, with arbitrary boundary conditions on the cavity surface. These theorems connect “downward wetting functions” and total cavity flow rates. Simple relations are established between scattering functions in the wave context and wetting functions in the soil water context. The important consequence is that flow rates for a large range of cavity shapes can be inferred simply and directly from extant results on forward scattering functions. It is proved that at large r (dimensionless radius), flow is concentrated in a small angular region vertically beneath the cavity and has a Gaussian distribution with angular standard deviation (sr)−½ (s=½αl; α, sorptive number; l, characteristic cavity length.)