Nonuniform Leaching from Nonuniform Steady Infiltration

The two‐dimensional quasilinear steady flow equation is solved exactly for arbitrary periodic distribution of surface source strength v 0 ( x ) ( x , horizontal coordinate), both for flow to infinite depth and to a water table at finite depth. Solutions are given both for the Kirchhoff variable ⊗ and the stream function φ. They are explored in detail forυ 0 = v ¯ 0 ( 1 + η   cos     π x / l ) ( 0 < η ≤ 1 ) . For each solution emphasis is placed on determining the limits on v 0 ( x ) which ensure that the moisture potential Ψ ⩽ 0, so that the quasilinear formulation is applicable. This essential precaution has sometimes been disregarded. The presence of a water table strongly influences ⊗, but has relatively little effect on φ. This makes possible important mathematical simplifications. Remarkably, simple exact solutions are found for travel times. They reveal singularities in the travel‐time functions overlooked in previous work using a finite difference method. For large times, the family of isochrones behaves like a travelling wave with shape and velocity constant. Streamlines and isochrones are compared for a coarse soil (parameter α = 25 m −1 ) and a fine one (α = 0.25 m −1 ). Surface velocity differentials persist much more strongly for the coarse soil, which exhibits much greater horizontal variation of travel times. By one measure, nonuniformity of leaching is 7.8 times greater in the coarse soil than the fine one. A previous study of problems of this class concluded incorrectly that leaching is more uniform for saturated than for unsaturated flow.