Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer

被引:106
作者
Verhoest, NEC
Troch, PA
机构
[1] State Univ Ghent, Lab Hydrol & Water Management, B-9000 Ghent, Belgium
[2] Wageningen Univ, Subdept Water Resources, NL-6709 AP Wageningen, Netherlands
关键词
D O I
10.1029/1999WR900317
中图分类号
X [环境科学、安全科学];
学科分类号
08 ; 0830 ;
摘要
Subsurface flow from a hillslope can be described by the hydraulic groundwater theory as formulated by the Boussinesq equation. Several attempts have been made to solve this partial differential equation, and exact solutions have been found for specific situations. In the case of a sloping aquifer, Brutsaert [1994] suggested linearizing the equation to calculate the unit response of the hillslope. In this paper we first apply the work of Brutsaert by assuming a constant recharge to the groundwater table. The solution describes the groundwater table levels and the outflow in function of time. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. This steady state water table is used as an initial condition to derive another analytical solution of the Boussinesq equation. This can then be used in a quasi steady state approach to compute outflow under changing recharge conditions.
引用
收藏
页码:793 / 800
页数:8
相关论文
共 22 条
[1]  
Arfken GeorgeB., 1995, Mathematical Methods for Physicists, Fourth Edition, VFourth
[2]  
Bear J., 1988, DYNAMICS FLUIDS PORO
[3]   KINEMATIC SUBSURFACE STORMFLOW [J].
BEVEN, K .
WATER RESOURCES RESEARCH, 1981, 17 (05) :1419-1424
[4]  
Boussinesq J., 1877, Acad. Sci. Inst. Fr., V23, P252
[5]  
Boussinesq J., 1904, J De Mathe Pures Et Appl, V10, P5
[6]   THE UNIT RESPONSE OF GROUNDWATER OUTFLOW FROM A HILLSLOPE [J].
BRUTSAERT, W .
WATER RESOURCES RESEARCH, 1994, 30 (10) :2759-2763
[7]   THE UNIT RESPONSE OF GROUNDWATER OUTFLOW FROM A HILLSLOPE - REPLY [J].
BRUTSAERT, W .
WATER RESOURCES RESEARCH, 1995, 31 (09) :2379-2380
[8]   REGIONALIZED DROUGHT FLOW HYDROGRAPHS FROM A MATURE GLACIATED PLATEAU [J].
BRUTSAERT, W ;
NIEBER, JL .
WATER RESOURCES RESEARCH, 1977, 13 (03) :637-644
[9]   THE UNIT RESPONSE OF GROUNDWATER OUTFLOW FROM A HILLSLOPE - COMMENT [J].
CHAPMAN, T .
WATER RESOURCES RESEARCH, 1995, 31 (09) :2377-2378
[10]   DRAINAGE OF GROUNDWATER RESTING ON A SLOPING BED [J].
CHILDS, EC .
WATER RESOURCES RESEARCH, 1971, 7 (05) :1256-&