Linearized time‐dependent infiltration from a shallow pond

Abstract

Time‐dependent quasi‐linearized infiltration with constant diffusivity from an axisymmetric shallow flat pond into a homogeneous semi‐infinite porous medium is investigated. Use of the Laplace transform reduces the equation to a form that can be solved using the boundary element method and inverted without difficulty. Previous attacks on this problem have been limited to solutions for large time because of the lack of a closed form expression for the axisymmetric free space Green's function. Here an alternative technique for evaluating the axisymmetric free space Green's function is presented, which enables solutions to be obtained at any time. Time‐varying fluxes are presented for a range of cavity sizes. The numerical results for small time match those predicted from one‐dimensional infiltration models, while the large time results approach the appropriate steady state values. The detailed numerical results indicate that approximate analytic results for fluxes from buried sources can be extended to include the shallow flat pond. This, together with earlier approximations for steady state fluxes, allows the flux from a shallow flat pond to be simply estimated at any time.