A Short Note on Self-Similar Solution to Unconfined Flow in an Aquifer with Accretion

Arieh Pistiner

Unit for Hydrocarbon Pollution Prevention, Ministry of the Environmental Protection, Haifa, Israel.

DOI: 10.4236/ojfd.2015.51007                

Abstract

In this study we refer to a non-steady state, one-dimensional (on the x-axis), unconfined and saturated flow in an aquifer, described by the Boussinesq equation, combined with accretion. In accordance with the above, the moving boundary of the saturated area (toward x → +∝) serves as a horizontal water flux source to the unsaturated area. As time advances, the horizontally saturated zone, lying on the x-axis, becomes wider. A self-similar solution is derived that, after some mathematical manipulation, it is described in terms of Hypergeometric functions. The long-time behaviors of the solution describe the situation at which the water flux, that penetrates horizontally to the non-saturated zone, is equal to the water flux entering into the saturated zone.

Keywords

Boussinesq Equation, Self-Similar Solution, Hypergeometric Function

Conflicts of Interest

The authors declare no conflicts of interest.

References

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