One-dimensional oscillatory flows in partially saturated media with moving multi-front

Abstract

International audienceThe moving multi-front (MMF) methods are used to analyze the response of partially saturated flow due to tidal periodic forcing imposed at the bottom of a vertical porous column comprising a saturated zone, a water table, and an unsaturated zone above it. The MMF is a Lagrangian semi-analytical method for solving the nonlinear Richards equation, based on a non-linear ordinary differential equations system, which is compared in this paper to a Eulerian finite volume solution. The MMF is used here to analyze the water table fluctuations Zs(t), the bottom flux fluctuations q0(t), as well as the vertical profiles of total head H(z,t), and finally, the complex behavior of the zero-flux planes Z0(t), during the cyclic motion. Additionally, the MMF is used to develop a parametric study of the mean water table height vs frequency. A systematic error analysis is developed for MMF vs the number of moving fronts (N), leading to a characterization of error norm for the space–time water content profiles (with second order accuracy) and for the temporal water table elevation (with order of accuracy 4/3). The MMF method is a generalization of the Green–Ampt piston flow approximation, which corresponds to a single moving front (N=1). The errors of the N-front MMF are rapidly reduced as the number of fronts increases. In many cases, 20 moving fronts are sufficient to capture most features. For sandy soils (fine sand), even the 2-front solution (N= 2) is satisfactory in terms of water table response Zs(t). Overall, the MMF method is a useful and efficient tool for exploring the frequency response of the water table and the unsaturated zone to tidal forcing