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Optimal Prediction of Saturation and Wetting Fronts during Trickle Irrigation
Author(s) -
Lockington D.,
Parlange J.Y.,
Surin A.
Publication year - 1984
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1984.03615995004800030003x
Subject(s) - saturation (graph theory) , wetting , porous medium , mathematics , nonlinear system , limit (mathematics) , diffusion , instability , richards equation , drip irrigation , simple (philosophy) , mathematical analysis , mechanics , porosity , soil water , thermodynamics , geotechnical engineering , physics , environmental science , irrigation , geology , soil science , ecology , philosophy , epistemology , combinatorics , quantum mechanics , biology
The nonlinear diffusion equation in spherical geometry describes water movement from a point source into a porous medium. This situation occurs, for example, in the early stages of trickle irrigation. Prediction of the saturation and wetting front positions during irrigation is of obvious practical importance. In the present paper, a general formula which predicts the positions of the two fronts is found by optimization. For particular soil properties the exact numerical solution of the diffusion equation can be easily found and is used to check the accuracy of the optimization formula. This formula proves to be extremely accurate. A simple asymptotic solution is also obtained which compares favorably with the above results in the long‐time limit. The maximum error associated with neglecting gravity is quantified using this solution and proves to be quite acceptable for most practical applications. In those few cases when this error is too large to be neglected and gravity needs to be included in the theory, other effects, e.g., instability, should also be considered.