[1] 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.
The effect of spatial variability of the hydraulic conductivity upon free-surface flow
is investigated in a stochastic framework. We examine the three-dimensional free-surface
gravitational flow problem for a sloped mean uniform flow in a randomly
heterogeneous porous medium. The model also describes the interface between two
fluids of differing densities, e.g. freshwater/saltwater and water/oil with the denser
fluid at rest. We develop analytic solutions for the variance and integral scale of
free-surface fluctuations and of specific discharge on the free surface. Additionally,
we obtain semi-analytic solutions for the statistical moments of the head and the
specific discharge beneath the free surface. Statistical moments are derived using a
first-order approximation and then compared with their counterpart in an unbounded
medium. The effect of anisotropy and angle of mean uniform flow on the statistical
moments is analysed. The solutions can be used for solving more complex flows,
slowly varying in the mean.
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