Recharge-induced groundwater flow over a plane sloping bed: Solutions for steady and transient flow using physical and numerical models

Water Resources Research

Volumn 41, Issue 7, 2005, Pages 1-11

  Chapman, T G ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA REDUCTION; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; SEEPAGE; VISCOUS FLOW;

BOUSSINESQ MODEL; FREE BOUNDARY PROBLEMS; UNIFORM RECHARGE; VISCOUS FLUID MODEL TESTS;

GROUNDWATER;

GROUNDWATER FLOW; NUMERICAL MODEL; RECHARGE; TRANSIENT FLOW;

EID: 23944445540     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2004WR003606     Document Type: Article

References (43)

1. Bear, J. (1960), Scales of viscous analogy models for ground water studies, J. Hydraul. Div. Am. Soc. Civ. Eng., 86, 11-23.
2. Bear, J. (1969), Flow Through Porous Media, Elsevier, New York.
3. Bear, J., D. Zaslavsky, and S. Irmay (1968), Physical Principles of Water Percolation and Seepage, United Nations Sci., Educ., and Cultural Organ., Paris.
4. Beven, K. (1981), Kinematic subsurface stormflow, Water Resour. Res., 17, 1419-1424.
5. Beven, K. (1982), On subsurface stormflow: Predictions with simple kinematic theory for saturated and unsaturated flows, Water Resour. Res., 18, 1627-1633.
6. Boussinesq, J. (1877), Essai sur la théorie des eaux courantes, Mem. Pres. Divers Savants Acad. Sci. Inst. Natl. Fr., 23, 680 pp.
7. Brutsaert, W. (1994), The unit response of ground water outflow from a hillslope, Water Resour. Res., 30, 2759-2763.
8. Chapman, T. G. (1980), Modelling groundwater flow over sloping beds, Water Resour. Res., 16, 1114-1118.
9. Chapman, T. G. (1999), A comparison of algorithms for stream flow recession and baseflow separation, Hydrol. Processes, 13, 701-714.
10. Chapman, T. G. (2003), Steady recharge-induced groundwater flow over a plane bed: Nonlinear and linear solutions, in MODSIM 2003 International Congress on Modelling and Simulation, vol. 1, pp. 254-259, Model, and Simul. Soc. of Aust. and N. Z., Townsville, Queensl.
11. Chapman, T. G., and R. F. Dressler (1984), Unsteady shallow groundwater flow over a curved impermeable boundary, Water Resour. Res., 20, 1427-1434.
12. Childs, E. C. (1971), Drainage of groundwater resting on a sloping bed, Water Resour. Res., 7, 1256-1263.
13. Dupuit, J. (1863), Etudes Théoretiques et Pratiques sur le Mouvement des Eaux, Dunod, Paris.
14. Guitjens, J. C., and J. N. Luthin (1965), Viscous model study of drain spacing on sloping land and comparison with mathematical solutions, Water Resour. Res., 1, 523-530.
15. Hele-Shaw, H. S. (1897), Experiments on the nature of the surface resistance in pipes and on ships, Trans. Inst. Nov. Archit., 39, 145-156.
16. Henderson, F. M., and R. A. Wooding (1964), Overland flow and groundwater flow from a steady rainfall of finite duration, J. Geophys. Res., 69, 1531-1540.
17. Ibrahim, H. A., and W. Brutsaert (1965), Inflow hydrographs from large unconfined aquifers, Proc. Irrig. Drain. Div. Am. Soc. Civ. Eng., 91, 21-38.
18. Jaiswal, C. S., and H. S. Chauhan (1975), A Hele-Shaw model study of steady state flow in an unconfined aquifer resting on a sloping bed, Water Resour. Res., 11, 595-600.
19. Koussis, A. D. (1992), A linear conceptual subsurface storm flow model, Water Resour. Res., 28, 1047-1052.
20. Koussis, A. D., and L.-T. Lien (1982), Linear theory of subsurface storm flow, Water Resour. Res., 18, 1738-1740.
21. Koussis, A. D., M. E. Smith, E. Akylas, and M. Tombrou (1998), Groundwater drainage flow in a soil layer resting on an inclined leaky bed, Water Resour. Res., 34, 2879-2887.
22. Luthin, J. N., and J. C. Guitjens (1967), Transient solutions for drainage of sloping lands, Proc. Amer. Soc. Civ. Eng., 93, 43-51.
23. Marei, S. M., and G. D. Towner (1975), A Hele-Shaw analog study of the seepage of groundwater resting on a sloping bed, Water Resour. Res., 11, 589-594.
24. Ong, G. (2003), Subsurface water flows over a curved impermeable bed, BE thesis, 134 pp., Univ. of New South Wales, Sydney, New South Wales, Australia.
25. Paniconi, C., P. A. Troch, E. E. van Loon, and A. G. J. Hilberts (2003), Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 2. Intercomparison with a three-dimensional Richards equation model, Water Resour. Res., 39(11), 1317, doi:10.1029/2002WR001730.
26. Pauwels, V. R. N., N. E. C. Verhoest, and F. P. D. Troch (2002), A meta-hillslope model based on an analytical solution to a linearized Boussinesq equation for temporally variable recharge rates, Water Resour. Res., 38(12), 1297, doi:10.1029/2001WR000714.
27. Pi, Z., and A. T. Hjelmfelt (1994), Hybrid finite analytic solution of lateral subsurface flow, Water Resour. Res., 30, 1471-1478.
28. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling (1989), Numerical Recipes, 702 pp., Cambridge Univ. Press, New York.
29. Ram, S., and H. S. Chauhan (1987), Analytical and experimental solutions from drainage of sloping lands with time-varying recharge, Water Resour. Res., 23, 1090-1096.
30. Schmid, P., and J. Luthin (1964), The drainage of sloping lands, J. Geophys. Res., 69, 1525-1529.
31. Sloan, W. T. (2000), A physics-based function for modeling transient groundwater discharge at the watershed scale, Water Resour. Res., 36, 225-241.
32. Sloane, P. G., and I. D. Moore (1984), Modeling subsurface stormflow on steeply sloping forested watersheds, Water Resour. Res., 20, 1815-1822.
33. Smiles, D. E., and J. H. Knight (1979), The transient water table beneath a leaking canal, J. Hydrol., 44, 149-162.
34. Smiles, D. E., and A. N. Stokes (1976), Periodic solutions of a nonlinear diffusion equation used in groundwater flow theory: Examination using a Hele-Shaw model, J. Hydrol., 31, 27-35.
35. Stagnitti, F., L. Li, J.-Y. Parlange, W. Brutsaert, D. A. Lockington, T. S. Steenhuis, M. B. Parlange, D. A. Barry, and W. L. Hogarth (2004), Drying front in a sloping aquifer: Nonlinear effects, Water Resour. Res., 40, W04601, doi:10.1029/2003WR002255.
36. Su, N. (1994), A formula for computation of time-varying recharge of groundwater, J. Hydrol., 160, 123-135.
37. Todd, D. K. (1959), Ground Water Hydrology, 336 pp., John Wiley, Hoboken, N. Y.
38. Towner, G. D. (1975), Drainage of groundwater resting on a sloping bed with uniform rainfall, Water Resour. Res., 11, 144-147.
39. Troch, P. A., C. Paniconi, and E. van Loon (2003), Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 1. Formulation and characteristic response, Water Resour. Res., 39(11), 1316, doi:10.1029/2002WR001728.
40. Verhoest, N. E., and P. A. Troch (2000), Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer, Water Resour. Res., 36, 793-800.
41. Wemer, P. W. (1957), Some problems in non-artesian ground-water flow, Eos Trans. AGU, 38, 511-518.
42. Wooding, R. A., and T. G. Chapman (1966), Groundwater flow over a sloping impermeable layer: 1. Application of the Dupuit-Forchheimer assumption, J. Geophys. Res., 71, 2895-2902.
43. Zhang, H., D. A. Baray, and G. C. Hocking (1999), Analysis of continuous and pulsed pumping of a phreatic aquifer, Adv. Water Resour., 22, 623-632.