Profiling Ponded Soil Surface in Saturated Seepage Into Drain-Line Sink: Kalashnikov's Method of Lateral Leaching Revisited

Abstract

Two boundary value problems are solved for potential steady-state 2-D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled with the aim of "uniformization" the velocity and travel time between this surface and a horizontal drain modelled by the sink. The complex potential domain is a half-strip, which is mapped onto a reference plane. Either the velocity magnitude or a vertical coordinate along the land surface are control variables. Either a complexified velocity or complex physical coordinate are reconstructed by solving mixed problems with the help of the Keldysh-Sedov formula via singular integrals, the kernel of which are the control functions. The flow nets, isotachs, and breakthrough curves are found by computer algebra routines. A designed soil hump above the drain ameliorates an unwanted "preferential flow" (shortcut) and improves leaching of salinized soil of a cropfield during a pre-cultivation season.