On some hydrodynamic models of drainage

Émikh, V. N.

doi:10.1016/0021-8928(79)90039-x

Cited by 3 publications

(3 citation statements)

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“…Below, we select shape-controlling functions g(ξ ) that satisfy conditions (7). Consequently, we obtain the so-called mixed BVP for ω (ζ ):…”

Section: Bvps With Control Of Velocity Along the Soil Surfacementioning

confidence: 99%

“…where α, β and a are positive parameters. Clearly, all functions of the family (13) obey conditions (7). Equation ( 9) with kernel ( 13) is integrated as follows:…”

Section: Bvps With Control Of Velocity Along the Soil Surfacementioning

confidence: 99%

“…Analytical solutions to several free boundary problems related to Kalashnikov's lateral leaching are obtained in a set of papers and a book by Emikh (e.g. [7][8][9][10][11]). Emikh ignored the shape depth of furrows in Figure 1(b) and found that for this simplest, zero-depth geometry of the leaching channel the phreatic line in Figure 1(b) 'overhangs' the sink (see [26] for terminology) and has (one branch) up to 2 inflexion points.…”

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confidence: 99%

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

Kacimov

2022

Eur. J. Appl. Math

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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.

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“…Below, we select shape-controlling functions g(ξ ) that satisfy conditions (7). Consequently, we obtain the so-called mixed BVP for ω (ζ ):…”

Section: Bvps With Control Of Velocity Along the Soil Surfacementioning

confidence: 99%

“…where α, β and a are positive parameters. Clearly, all functions of the family (13) obey conditions (7). Equation ( 9) with kernel ( 13) is integrated as follows:…”

Section: Bvps With Control Of Velocity Along the Soil Surfacementioning

confidence: 99%