WETTING FRONTS IN ONE-DIMENSIONAL PERIODICALLY LAYERED SOILS

We study wetting front (traveling wave) solutions to the Richards equa tion that describe the vertical infiltration of water through one-dime nsional periodically layered unsaturated soils. We prove the existence , uniqueness, and large time asymptotic stability of the traveling wav e solutions under prescribed flux boundary conditions and certain cons titutive conditions. The traveling waves are connections between two s teady state solutions that form near the ground surface and towards th e underground water table. We found a closed form expression of the wa ve speed. The speed of a traveling wave is equal to the ratio of the f lux difference and the difference of the spatial averages of the two s teady states. We give both analytical and numerical examples showing t hat the wave speeds in the periodic soils can be larger or smaller tha n those in the homogeneous soils which have the same mean diffusivity and conductivity. In our examples, if the phases of inhomogeneities in diffusivity and conductivity functions differ by half the period, the n the periodic soils speed up the waves; if the phases are the same, t hen the periodic soils slow down the waves. We also present numerical solutions to the Richards equation using the finite difference method in regimes where our constitutive conditions are no longer valid, and we observe similar stable fronts.