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

• 作者: Arieh Pistiner
• 来源期刊: 流体动力学(英文)
• 学科: 数学
• 关键词: BOUSSINESQ Equation SELF-SIMILAR Solution HYPERGEOMETRIC Function
• 年，卷（期）: 2015,（1）
• 页码范围: 51-57
• 页数: 7页
• 分类号: O1

摘要

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.