Profiling ponded soil surface in saturated seepage into drain-line sink: Kalashnikov's method of lateral leaching revisited

A. R. Kacimov, Yu U.V. Obnosov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)367-384
Number of pages18
JournalEuropean Journal of Applied Mathematics
Issue number2
Publication statusPublished - Jul 12 2022


  • 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

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