Two boundary value problems are solved for potential steady-state 2D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled. The aim of this shaping is 'uniformisation' of the velocity and travel time between this surface and a horizontal drain modelled by a line 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 is reconstructed by solving mixed boundary-value 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 salinised soil of a cropfield during a pre-cultivation season.
- Advective travel time along streamlines and breakthrough curve
- Reconstruction of holomorphic functions (complex potential, physical coordinate and complexified velocity) via the Keldysh-Sedov formulae
- Seepage from undulated ponded soil surface to periodic drains-sinks
ASJC Scopus subject areas
- Applied Mathematics