Wetting fronts in one-dimensional periodically layered soils.

In this thesis, we study traveling wave solutions to Richards equation in diffusive form which describes wetting fronts in vertical infiltration of water into one-dimensional periodically layered soils. We prove the existence and uniqueness of traveling waves solutions under prescribed flux boundary conditions and certain constitutive conditions on the diffusivity and conductivity functions in the equation. Furthermore, we show the long time stability of these traveling wave solutions under these conditions. The traveling waves are connections between two steady states that form near the ground surface and deep in the soil. We derive an analytical formula for the speed of these traveling waves which depends on the prescribed boundary fluxes and the steady states. Both analytical and numerical examples are found which show that the wave speed in a periodically layered soil may be slower, the same, or faster than the speed in a homogeneous soil. In these examples, if the phases of the diffusivity and conductivity functions are the same, the periodic soils slow down the waves. If the phases differ by half a period, the periodic soils speed up the waves. We also present numerical solutions to Richards equation using a finite difference method to address cases where our constitutive conditions do not hold. Similar stable wetting fronts are observed even in these cases