Time‐dependent, linearized two‐dimensional infiltration and evaporation from nonuniform and nonperiodic strip sources

Using a linearized equation describing unsaturated homogeneous and isotropic porous media flow, a general, two‐dimensional, time‐dependent mathematical model is presented for infiltration and/or infiltration‐evaporation from nonuniform and nonperiodic 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 in an integral form for the distribution of matric flux potential has been obtained. The result of Warrick and Lomen (1976) for a single strip source is shown to be a special case of this general model. The solution for infiltration from two strip sources is presented as another special case. Also, a third special case is presented for infiltration from two strip sources and evaporation from another strip located in the middle part. The horizontal and vertical flux components for these cases are presented. All results are expressed in integral forms and calculated with a computer using a numerical integration method. The solutions predict the matric flux potential and flux components as functions of space and time. Examples that illustrate the applicability of some of the solutions are presented. These solutions are of interest in the design of both sprinkler and furrow irrigation systems. The results may also be used for different purposes in civil and agricultural engineering applications.