Unsaturated seepage flow from a horizontal boundary
Author:
R. A. Wooding
Journal:
Quart. Appl. Math. 33 (1975), 143-159
DOI:
https://doi.org/10.1090/qam/99670
MathSciNet review:
QAM99670
Full-text PDF Free Access
References |
Additional Information
J. R. Philip, Theory of infiltration, Adv. Hydrosci. 5, 215–296 (1969)
C. Braester, G. Dagan, S. Neuman and D. Zaslavsky, A survey of the equations and solutions of unsaturated flow in porous media, 1st Ann. Rep. (Part 1), Project No. A10-SWC-77, Technion—Israel Institute of Technology, 1971
A. Poulovassilis and E. C. Childs, The hysteresis of pore water: The non-independence of domains, Soil Sci. 112, 301–312 (1971)
G. C. Topp, Soil-water hysteresis: The domain theory extended to pore interaction conditions, Soil Sci. Soc. Amer. Proc. 35, 219–225 (1971)
G. A. Turner, The flow-structure in packed beds, Chem. Eng. Sci. 7, 156–165 (1958)
D. E. Hill and J. -Y. Parlange, Wetting front instability in layered soils, Soi Sci. Soc. Amer. Proc. 36, 697–702 (1972)
H. J. Morel-Seytoux, Introduction to flow of immiscible liquids in porous media, ’Flow Through Porous Media’, ed. by R. J. M. De Wiest Academic Press, New York, 455–516 (1969)
A. J. Peck, Moisture profile development and air compression during water uptake by bounded porous bodies. 3. Vertical columns, Soil Sci. 100, 44–51 (1965)
J. -Y. Parlange, Theory of water-movement in soils: I. One-dimensional absorption, Soil Sci. 111, 134–137 (1971)
J. -Y. Parlange, Theory of water-movement in soils: II. One-dimensional infiltration, Soil Sci. 1ll, 170–174 (1971)
A. Noblanc and H. J. Morel-Seytoux, Perturbation analysis of two-phase infiltration, J. Hydraul. Div. Proc. ASCE, 98 (HY9), 127–1541 (1972)
R. A. Wooding, Perturbation analysis of the equation for the transport of dissolved solids through porous media. II. Basic non-linear problem. J. Hydrol. (Amsterdam) 16, 105–116
- M. J. Lighthill and G. B. Whitham, On kinematic waves. I. Flood movement in long rivers, Proc. Roy. Soc. London Ser. A 229 (1955), 281–316. MR 72605, DOI https://doi.org/10.1098/rspa.1955.0088
- M. J. Lighthill, Viscosity effects in sound waves of finite amplitude, Surveys in mechanics, Cambridge, at the University Press, 1956, pp. 250–351 (2 plates). MR 0077346
G. C. Topp and E. E. Miller, Hysteretic moisture characteristics and hydraulic conductivities for glass-bead media, Soil Sci. Soc. Amer. Proc. 30, 156–162 (1966)
G. C. Topp, Soil-water hysteresis measured in a sandy loam and compared with the hysteretic domain model, Soil Sci. Soc. Amer. Proc. 33, 645–651 (1969)
G. C. Topp, Soil water hysteresis in silt loam and clay loam soils, Water Resources Res. 7, 914–920 (1971)
J. A. Enderby, The domain model of hysteresis. I. Independent domains, Trans. Faraday Soc. 51, 835–848 (1955)
D. H. Everett, A general approach to hysteresis. 4. An alternative formulation of the domain model, Trans. Faraday Soc. 51, 1551–1557 (1955)
D. H. Everett, Adsorption hysteresis, ’Solid Gas Interface’ ed. E. Alison Flood, 2, 1055–1113 (1967)
W. R. Gardner, Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table, Soil Science, 85, 244–249 (1958)
J. R. Philip, Steady infiltration from buried point sources and spherical cavities, Water Resources Res. 4, 1039–1047 (1968)
R. A. Wooding, Steady infiltration from a shallow circular pond, Water Resources Res. 4, 1259–1273 (1968)
R. A. Wooding, Perturbation analysis of the equation for the transport of dissolved solids through porous media. I. Linear problems, J. Hydrol. (Amsterdam) 16, 1—16 (1972)
- Milton Van Dyke, Perturbation methods in fluid mechanics, Applied Mathematics and Mechanics, Vol. 8, Academic Press, New York-London, 1964. MR 0176702
- Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0246537
- L. Crocco, Coordinate perturbation and multiple scale in gasdynamics, Philos. Trans. Roy. Soc. London Ser. A 272 (1972), 275–301. MR 334682, DOI https://doi.org/10.1098/rsta.1972.0051
J. R. Philip, Theory of infiltration, Adv. Hydrosci. 5, 215–296 (1969)
C. Braester, G. Dagan, S. Neuman and D. Zaslavsky, A survey of the equations and solutions of unsaturated flow in porous media, 1st Ann. Rep. (Part 1), Project No. A10-SWC-77, Technion—Israel Institute of Technology, 1971
A. Poulovassilis and E. C. Childs, The hysteresis of pore water: The non-independence of domains, Soil Sci. 112, 301–312 (1971)
G. C. Topp, Soil-water hysteresis: The domain theory extended to pore interaction conditions, Soil Sci. Soc. Amer. Proc. 35, 219–225 (1971)
G. A. Turner, The flow-structure in packed beds, Chem. Eng. Sci. 7, 156–165 (1958)
D. E. Hill and J. -Y. Parlange, Wetting front instability in layered soils, Soi Sci. Soc. Amer. Proc. 36, 697–702 (1972)
H. J. Morel-Seytoux, Introduction to flow of immiscible liquids in porous media, ’Flow Through Porous Media’, ed. by R. J. M. De Wiest Academic Press, New York, 455–516 (1969)
A. J. Peck, Moisture profile development and air compression during water uptake by bounded porous bodies. 3. Vertical columns, Soil Sci. 100, 44–51 (1965)
J. -Y. Parlange, Theory of water-movement in soils: I. One-dimensional absorption, Soil Sci. 111, 134–137 (1971)
J. -Y. Parlange, Theory of water-movement in soils: II. One-dimensional infiltration, Soil Sci. 1ll, 170–174 (1971)
A. Noblanc and H. J. Morel-Seytoux, Perturbation analysis of two-phase infiltration, J. Hydraul. Div. Proc. ASCE, 98 (HY9), 127–1541 (1972)
R. A. Wooding, Perturbation analysis of the equation for the transport of dissolved solids through porous media. II. Basic non-linear problem. J. Hydrol. (Amsterdam) 16, 105–116
M. J. Lighthill and G. B. Whitham, On kinematic waves. I. Flood movement in long rivers, Proc. Roy. Soc. A 229, 281–316 (1955)
M. J. Lighthill, Viscosity effects in sound waves of finite amplitude, ’Surveys in Mechanics’ eds. G. K. Batchelor and R. M. Davies, University Press, Cambridge, 250–351 (1956)
G. C. Topp and E. E. Miller, Hysteretic moisture characteristics and hydraulic conductivities for glass-bead media, Soil Sci. Soc. Amer. Proc. 30, 156–162 (1966)
G. C. Topp, Soil-water hysteresis measured in a sandy loam and compared with the hysteretic domain model, Soil Sci. Soc. Amer. Proc. 33, 645–651 (1969)
G. C. Topp, Soil water hysteresis in silt loam and clay loam soils, Water Resources Res. 7, 914–920 (1971)
J. A. Enderby, The domain model of hysteresis. I. Independent domains, Trans. Faraday Soc. 51, 835–848 (1955)
D. H. Everett, A general approach to hysteresis. 4. An alternative formulation of the domain model, Trans. Faraday Soc. 51, 1551–1557 (1955)
D. H. Everett, Adsorption hysteresis, ’Solid Gas Interface’ ed. E. Alison Flood, 2, 1055–1113 (1967)
W. R. Gardner, Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table, Soil Science, 85, 244–249 (1958)
J. R. Philip, Steady infiltration from buried point sources and spherical cavities, Water Resources Res. 4, 1039–1047 (1968)
R. A. Wooding, Steady infiltration from a shallow circular pond, Water Resources Res. 4, 1259–1273 (1968)
R. A. Wooding, Perturbation analysis of the equation for the transport of dissolved solids through porous media. I. Linear problems, J. Hydrol. (Amsterdam) 16, 1—16 (1972)
M. Van Dyke, Perturbation methods in fluid mechanics, Academic Press, New York, 1964
J. D. Cole, Perturbation methods in applied mathematics. Blaisdell, Waltham, Mass., 1968
L. Crocco, Coordinate perturbation and multiple scale in gas-dynamics, Phil. Trans. Roy. Soc. A. 272, 275–301 (1972)
Additional Information
Article copyright:
© Copyright 1975
American Mathematical Society
