Generalized Green-Ampt Approach to 1D Oscillatory Flows in Partially Saturated/Unsaturated Media: Capillary Effects in Beach Hydrodynamics (Semi-analytical & Numerical studies)

Semi-analytical multi-front solutions of water table response due to periodic forcing in a partially saturated vertical porous column are developed, tested and compared to finite volume solutions of the Richards equation. The multi-front solutions are useful for capturing parametrically the frequency response of the vertical column to tidal oscillations while taking into account both capillary and gravitational effects. Vertical oscillations are examined, accounting for unsaturated flow above the oscillating water table as well as saturated flow below it. The multi-front models are conceived as successive generalizations of the Green-Ampt piston flow approach. The single front model is an "inverted" Green Ampt model, with an abrupt front separating the saturated and dry regions. It is adapted to the case of an oscillatory pressure imposed at the bottom of the column (rather than a fixed pressure imposed at the top). The N front models (N>=2) further generalize this concept, using a (Theta(h), K(h)) parametrization to take into account the capillary properties of the unsaturated medium. The resulting systems of ODE's are non linear with time variable coefficients. The solutions obtained for N = 10 fronts are satisfactory both in terms of water table fluctuations and moisture profiles, even for fine grained soils (Guelph Loam). They are computed much faster than space-time discretized solutions of the non linear Richards PDE. For sandy soils, even the 2-front solution (N=2) is satisfactory in terms of water table response Zs(t). The 2-front model itself is a significant improvement on the single front Green-Ampt model, and it appears potentially useful for analyzing the response of unsaturated flow systems under various types of oscillatory and transient forcing. Overall, the N-front method is useful for exploring the frequency response of the water table to tidal forcing.