On the nonlinear stability analysis of the wetting front in the vadose zone

The goal of this research is to explore Wetting Front Instability in the vadose zone. We will begin by performing a linear stability analysis of the Richards Equation. For a special case of boundary conditions and general exponential constitutive relations we found that the Richards Equation is unconditionally stable.;Also in this thesis we present a linear stability analysis of the Hold-Back-Pile-Up Richards Equation to show that it is able to model gravity driven fingers in the vadose zone. The stability of the Hold-Back-Pile-Up Richards Equation is also studied using a generalized energy method. A Lyapunov functional is identified and the perturbations are shown to be asymptotically, exponentially stable in this measure, provided that NG (capillary-gravity ratio) is sufficiently small.