Interaction of Stream and Sloping Aquifer Receiving Constant Recharge
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VIEW THE REPLYPublication: Journal of Irrigation and Drainage Engineering
Volume 127, Issue 5
Abstract
An analytical solution and finite-element numerical solution of a linearized and nonlinear Boussinesq equation, respectively, were obtained to describe water table variation in a semi-infinite sloping/horizontal aquifer caused by the sudden rise or fall of the water level in the adjoining stream. Transient water table profiles in recharging and discharging aquifers having 0, 5, and 10% slopes and receiving zero or constant replenishment from the land surface were computed for t = 1 and 5 days by employing analytical and finite-element numerical solutions. The effect of linearization of the nonlinear governing equation, recharge, and slope of the impermeable barrier on water table variation in a semi-infinite flow region was illustrated with the help of a numerical example. Results suggest that linearization of the nonlinear equation has only a marginal impact on the predicted water table heights (with or without considering constant replenishment). The relative errors between the analytical and finite-element numerical solution varied in the range of −0.39 to 1.59%. An increase in slope of the impermeable barrier causes an increase in the water table height at all the horizontal locations, except at the boundaries for the recharging case and a decrease for the discharging case.
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References
1.
Boussinesq, J. ( 1904). “Recherches theoretiques sur l'ecoulement des nappes d'eau infiltrees dans le sol et sur le debit des sources.” J. de Math, Pures et Appl., Series 5, Tome X, 5–78 (in French).
2.
Carslaw, H. S., and Jaeger, J. C. ( 1959). Conduction of heat in solids, 2nd Ed., Oxford at the Clarendon Press, London.
3.
Edelman, F. ( 1947). “Over de berekening van ground water stromingen.” PhD thesis, University of Delft, Delft, The Netherlands (in Dutch).
4.
Hornberger, G. M., Ebert, J., and Remson, I. ( 1970). “Numerical solution of the Boussinesq equation for aquifer-stream interaction.” Water Resour. Res., 6(2), 601–608.
5.
Lockington, D. A. (1997). “Response of unconfined aquifer to sudden change in boundary head.”J. Irrig. and Drain. Engrg., ASCE, 123(1), 24–27.
6.
Maasland, M. ( 1959). “Water table fluctuations induced by intermittent recharge.” J. Geophys. Res., 64(5), 549–559.
7.
Marino, M. A. ( 1973). “Water table fluctuation in semipervious stream-unconfined aquifer systems.” J. Hydro., Amsterdam, 19, 43–52.
8.
Ozisik, M. N. ( 1980). Heat conduction, Wiley, New York.
9.
Pinder, G. F., and Gray, W. G. ( 1977). Finite element simulation in surface and subsurface hydrology, Academic, New York.
10.
Polubarinova-Kochina, P. Ya. ( 1948). “On a non-linear partial differential equation, occurring in seepage theory.” Doklady Akademii Nauk, 36(6) (in Russian).
11.
Polubarinova-Kochina, P. Ya. ( 1949). “On unsteady flow of ground water seeping from reservoirs.” Prikladnaya Mathematika i Makhanika, 13(2) (in Russian).
12.
Polubarinova-Kochina, P. Ya. ( 1962). Theory of ground water movement, J. M. R. de Wiest, translator, Princeton University Press, Princeton, N.J.
13.
Prenter, P. M. ( 1975). Spline and variational methods, Wiley, New York.
14.
Serrano, S. E., and Workman, S. R. ( 1998). “Modelling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution.” J. Hydro., Amsterdam, 206, 245–255.
15.
Sidiropoulos, E., Asce, A. M., Tzimopoulos, C., and Tolikas, P. (1984). “Analytical treatment of unsteady horizontal seepage.”J. Hydr. Engrg., ASCE, 110(11), 1659–1670.
16.
Tolikas, P. K., Sidiropoulos, E. G., and Tzimopoulos, C. D. ( 1984). “A simple analytical solution for the Boussinesq one-dimensional ground water flow equation.” Water Resour. Res., 20(1), 24–28.
17.
Upadhyaya, A. ( 1999). “Mathematical modelling of water table fluctuations in sloping aquifers.” PhD thesis, G. B. Pant University of Agriculture and Technology, Pantnagar, India.
18.
Upadhyaya, A., and Chauhan, H. S. (1998). “Comparison of numerical and analytical solutions of Boussinesq equation in semi-infinite flow region.”J. Irrig. and Drain. Engrg., ASCE, 124(5), 265–270.
19.
Verigin, N. N. ( 1949). “On unsteady flow of ground water near reservoirs.” Doklady Akademii Nauk, 66(6) (in Russian).
20.
Werner, P. W. ( 1953). “On non-artesian ground water flow.” Geofis pura Appl., 25, 37–43.
21.
Werner, P. W. ( 1957). “Some problems in non-artesian ground water flow.” Trans. Am. Geophys. Union, 38(4), 511–518.
22.
Workman, S. R., Serrano, S. E., and Liberty, K. ( 1997). “Development and application of an analytical model of stream/aquifer interaction.” J. Hydro., Amsterdam, 200, 149–164.
23.
Yussuff, S. M. H., Chauhan, H. S., Kumar, M., and Srivastava, V. K. (1994). “Transient canal seepage to sloping aquifer.”J. Irrig. and Drain. Engrg., 120(1), 97–109.
24.
Zucker, M. B., Remson, I., Ebert, J., and Aguado, E. ( 1973). “Hydrologic studies using the Boussinesq equation with a recharge term.” Water Resour. Res., 9(3), 586–592.
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Received: Aug 29, 2000
Published online: Oct 1, 2001
Published in print: Oct 2001
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