Abstract
For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batu, V.: 1978, Steady infiltration from single and periodic strip sources,Soil Sci. Soc. Am. J. 42, 544–549.
Carrier, G. F. and Pearson, C. E.: 1991,Ordinary Differential Equations. SIAM, Philadelphia.
Churchill, R. V.: 1987,Fourier Series and Boundary Value Problems, 4th edn, McGraw-Hill, New York.
Gardner, W.: 1958, Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a watertable,Soil Sci. 85, 228–232.
Gilbarg, D. and Trudinger, N. S.: 1983,Elliptic Partial Differential Equations of Second Order, 2nd edn, Springer-Verlag, Berlin.
Customer Relations: 1991,FORTRAN Subroutines for Mathematical Applications, IMSL, Inc., Houston.
Mandal, A. C. and Waechter, R. T.: 1993, Steady infiltration from a semicircular cylindrical trench and a hemispherical pond into unsaturated soil,Water Resour. Res. 29, 457–467.
Philip, J. R.: 1968, Steady infiltration from buried point sources and spherical cavities,Water Resour. Res. 4, 1039–1047.
Philip, J. R.: 1969, Theory of infiltration,Adv. Hydrosci. 5, 215–296.
Philip, J. R.: 1984, Steady infiltration from circular cylindrical cavities,Soil Sci. Soc. Am. J. 48, 270–278.
Philip, J. R.: 1984, Nonuniform leaching from nonuniform steady infiltration,Soil Sci. Soc. Am. J. 48, 740–749.
Philip, J. R., Knight, J. H. and Waechter, R. T.: 1989, Unsaturated seepage and subterranean holes: conspectus, and exclusion problem for circular cylindrical cavities,Water Resour. Res. 25, 16–28.
Pullan, A. J.: 1990, The quasilinear approximation for unsaturated porous media flow,Water Resour. Res. 26, 1219–1234.
Raats, P. A. C.: 1970, Steady infiltration from line sources and furrows,Soil Soc. Am. Proc. 34, 709–714.
Read, W. W.: 1993, Series solutions for Laplace's equation with non-homogeneous mixed boundary conditions and irregular boundaries,Mathematical and Computer Modelling 17, 9–19; Errata,18, 107.
Read, W. W. and Volker, R. E.: 1993, Series solutions for steady seepage through hillsides with arbitrary flow boundaries,Water Resour. Res. 29, 2871–2880.
Wooding, R. A.: 1968, Steady infiltration from a shallow circular pond,Water Resour. Res. 4, 1259–1273.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Read, W., Broadbridge, P. Series solutions for steady unsaturated flow in irregular porous domains. Transp Porous Med 22, 195–214 (1996). https://doi.org/10.1007/BF01143515
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01143515