Uniform steady free surface flow with recharge in heterogeneous porous formations

Abstract

Free surface flow in a randomly heterogeneous medium with recharge is studied in a stochastic setting. A three‐dimensional gravitational flow model with sloped mean uniform flow is used to describe flow in a phreatic aquifer experiencing natural gradient flow, far from wells. The model seeks to investigate the effects of medium heterogeneity and recharge on flow on and below the free surface. Statistical moments of free surface position, head, and specific discharge are derived using a first‐order approximation and compared with their parallel in an unbounded medium. Analytic solutions for the variance of free surface fluctuations and of the specific discharge on the free surface are developed as well as semianalytic solutions for the statistical moments of head and specific discharge beneath the free surface. The effect of recharge, angle of mean free surface and anisotropy on the statistical moments is analyzed.