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Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface
Author(s) -
Basha H. A.
Publication year - 1999
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 - 10.1029/1998wr900015
Subject(s) - infiltration (hvac) , water content , boundary value problem , mathematics , porous medium , exponential function , moisture , richards equation , hydraulic conductivity , soil water , mathematical analysis , geotechnical engineering , mechanics , soil science , porosity , environmental science , thermodynamics , geology , physics , meteorology
The present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure. The Green's function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi‐infinite flow domain with arbitrary initial conditions, boundary conditions, and root‐uptake forcing functions and for various simple source geometry. The general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation, evaporation, root uptake, and moisture redistribution can be easily deduced from the general analytical model. The model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest. New explicit solutions have been obtained for one‐dimensional infiltration under various prescribed time‐dependent flux boundary conditions and for two‐ and three‐dimensional moisture redistribution. For constant initial or boundary conditions, the multidimensional solution is essentially the product of two or three time‐dependent terms with each term being a function of only one space variable.