TITLE:
A Short Note on Self-Similar Solution to Unconfined Flow in an Aquifer with Accretion
AUTHORS:
Arieh Pistiner
KEYWORDS:
Boussinesq Equation, Self-Similar Solution, Hypergeometric Function
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.5 No.1,
March
2,
2015
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.