TY - JOUR
T1 - Profiling ponded soil surface in saturated seepage into drain-line sink
T2 - Kalashnikov's method of lateral leaching revisited
AU - Kacimov, A. R.
AU - Obnosov, Yu U.V.
N1 - Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.
PY - 2022/7/12
Y1 - 2022/7/12
N2 - 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.
AB - 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.
KW - Advective travel time along streamlines and breakthrough curve
KW - Reconstruction of holomorphic functions (complex potential, physical coordinate and complexified velocity) via the Keldysh-Sedov formulae
KW - Seepage from undulated ponded soil surface to periodic drains-sinks
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U2 - 10.1017/S0956792522000171
DO - 10.1017/S0956792522000171
M3 - Article
AN - SCOPUS:85151529991
SN - 0956-7925
VL - 34
SP - 367
EP - 384
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 2
ER -