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Time‐dependent linearized two‐dimensional infiltration and evaporation from nonuniform and periodic strip sources
Author(s) -
Batu Vedat
Publication year - 1983
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/wr019i006p01523
Subject(s) - infiltration (hvac) , laplace transform , hydraulic conductivity , mathematics , mathematical analysis , isotropy , vadose zone , mechanics , geotechnical engineering , soil water , soil science , geology , physics , thermodynamics , quantum mechanics
Using a linearized partial differential equation describing unsaturated, homogeneous, and isotropic porous media flow, a general two‐dimensional time‐dependent mathematical model is presented for infiltration and infiltration‐evaporation cases from nonuniform and periodic strip sources located at the soil surface. The analysis is based on an exponential relationship between the unsaturated hydraulic conductivity and the soil water pressure head and also assumes a constant value for the derivative of unsaturated hydraulic conductivity with respect to water content. In the mathematical analysis, Laplace transform and Fourier analysis techniques are used simultaneously, and a general equation is obtained in series‐integral form for the distribution of matric flux potential. The solution for uniform infiltration from equally spaced strip sources and uniform evaporation from the rest of the strips is presented as a special case of the general model. Another special case is presented for infiltration from equally spaced strip sources. The results of this latter case are compared with Warrick and Lomen (1976), and it is observed that the agreement is reasonably good. All results are expressed in integral forms and are calculated by using a numerical integration method. Equations for the horizontal and vertical flux components for the special case are presented. The solutions predict the matric flux potential and flux components as functions of space and time. They are of interest in the design of irrigation systems and may be used also for different purposes in other engineering applications.