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Multidimensional steady infiltration with prescribed boundary conditions at the soil surface
Author(s) -
Basha H. A.
Publication year - 1994
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/94wr00484
Subject(s) - infiltration (hvac) , boundary value problem , exponential function , mathematics , mathematical analysis , inverse problem , porous medium , richards equation , inverse , soil water , geometry , geotechnical engineering , porosity , physics , soil science , geology , thermodynamics
The present work explores a class of analytical solutions of steady moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity. The Green's function method is used to derive a general analytical model which can handle multidimensional steady infiltration problems in a semi‐infinite medium with arbitrary boundary conditions and root uptake forcing functions and for various simple source geometries. The power of the Green's function method is such that a number of new problems were amenable to analysis and solutions to problems already solved were obtained in a form better suited for numerical computation. Of special importance is the capability of the analytical model to handle the difficult problem of mixed boundary conditions in an approximative fashion. The general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation, root uptake, and isothermal evaporation can be easily deduced. New solutions include the case of surface sources under a prescribed exponential head and flux distribution, an inverse power flux distribution, and periodic root uptake. The inverse power flux distribution allows the approximate modeling of constant potential sources with evaporation at the nonwetted surfaces. It is shown that all two‐ and three‐dimensional infiltration solutions are essentially integrals of two functions: one dependent on the geometry and distribution of the source and the other dependent on the boundary condition at the land surface. Near‐field and far‐field approximations have also been obtained and simple algebraic equations have been derived for the flux and potential beneath the centerline of the source. The proposed model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest in civil and agricultural engineering.