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- Title
Appropriate Boundary Condition for Dupuit‐Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge.
- Authors
Wu, Ying‐Hsin; Sayama, Takahiro; Nakakita, Eiichi
- Abstract
The application of Dupuit‐Boussinesq theory on the two‐dimensional steady groundwater flow in an unconfined sloping aquifer with uniform recharge is theoretically investigated. The examination of conditions at the downstream and upstream is performed. The method of phase plane is used to geometrically interpret the characteristics of the nonlinear theory by various initial conditions. For phase portrait analysis, three configurations for aquifers are considered. In each type of aquifer three conditions of recharges as well as downstream groundwater tables are also considered for comprehensive analysis. Based on the phase portrait analysis, one explicit formula in terms of known parameters and downstream boundary condition is derived to easily and straightforwardly determine an appropriate upstream boundary condition. The derived explicit formula can facilitate correct modeling using Boussinesq theory. Plain Language Summary: Groundwater is an important component affecting the human life and ecosystem on aspects of drinking water supply, food production, and many environmental processes. As is stored underground, groundwater distribution is always a puzzle to find out. In a hillslope groundwater table information can be measured at a certain location by monitoring techniques, but information uphill nearby is not directly accessible. For possibly knowing the unknown groundwater table, one of conventional ways is computation on sophisticated groundwater theories with some field parameters. However, as requiring high‐level knowledge in computation as well as groundwater theories, correct calculation is not easily achievable without expertise in both. To overcome this difficulty, with careful mathematical investigation, we propose a simple formula to judge whether a steady groundwater table exists at the upside of a sloping and soil‐mantled hillslope in terms of parameters of hillslope inclination, rain rate, and hydrological property of hillslope soil. This formula can intuitively facilitate correct assessing of groundwater table. Key Points: The nonlinear characteristics of groundwater flow in an unconfined Boussinesq aquifer are analyzed by using the method of phase planeAppropriate boundary conditions at the downstream and upstream boundaries are examinedAn explicit formula to determine the appropriate upstream boundary condition is derived
- Subjects
BOUNDARY value problems; AQUIFERS
- Publication
Water Resources Research, 2018, Vol 54, Issue 9, p5933
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/2018WR023070