Steady Darcian Flow in Subsurface Irrigation of Topsoil Impeded by a Substratum: Kornev-Riesenkampf-Philip Legacies Revisited

Yu V. Obnosov, A. R. Kacimov

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Flows in homogeneous topsoils with a subjacent substratum or horizontal groundwater table generated by line-point emitters are studied and tracked back to the Kornev method of subsurface irrigation. Laplace's equation governs flow in a saturated or tension-saturated hat-shaped zone subtended by the substratum, provided pressure in a porous pipe or mole hole is positive. For low capillarity a free surface (phreatic line or capillary fringe) and a layer-substratum interface of a constant vertical component of velocity bound the flow domain. The free surface is found for various values of source strengths, emitter elevation above the substratum and the ratio of hydraulic conductivities of the topsoil and substratum. Subcritical and supercritical regimes are distinguished. In the limit of an impermeable substratum, the Riesenkampf solution for a line source is analysed. In soils of high capillarity, the J.R. Philip model of a point source and 'exponential mirror principle' give a series solution for a vertical array of alternating sources and sinks. Four topological situations emerge, depending on the layer thicknesses, topsoil potential, source depths strengths, saturated conductivity and sorptive number. The point source, groundwater table and soil surface are hydrologically intertwined, with formation of dividing surfaces (separatrices) and critical lines.

Original languageEnglish
JournalIrrigation and Drainage
DOIs
Publication statusAccepted/In press - Jan 1 2018

Fingerprint

steady flow
subsurface irrigation
topsoil
capillarity
emitters (equipment)
irrigation
strength (mechanics)
water table
point source
capillary fringe
saturated flow
groundwater
pipes
hydraulic conductivity
soil
soil surface
conductivity
pipe
methodology

Keywords

  • Advective-dispersion equation
  • Emitter
  • Kirchhoff potential
  • Laplace's equation
  • Method of images
  • Water productivity
  • Water productivity

ASJC Scopus subject areas

  • Agronomy and Crop Science
  • Soil Science

Cite this

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title = "Steady Darcian Flow in Subsurface Irrigation of Topsoil Impeded by a Substratum: Kornev-Riesenkampf-Philip Legacies Revisited",
abstract = "Flows in homogeneous topsoils with a subjacent substratum or horizontal groundwater table generated by line-point emitters are studied and tracked back to the Kornev method of subsurface irrigation. Laplace's equation governs flow in a saturated or tension-saturated hat-shaped zone subtended by the substratum, provided pressure in a porous pipe or mole hole is positive. For low capillarity a free surface (phreatic line or capillary fringe) and a layer-substratum interface of a constant vertical component of velocity bound the flow domain. The free surface is found for various values of source strengths, emitter elevation above the substratum and the ratio of hydraulic conductivities of the topsoil and substratum. Subcritical and supercritical regimes are distinguished. In the limit of an impermeable substratum, the Riesenkampf solution for a line source is analysed. In soils of high capillarity, the J.R. Philip model of a point source and 'exponential mirror principle' give a series solution for a vertical array of alternating sources and sinks. Four topological situations emerge, depending on the layer thicknesses, topsoil potential, source depths strengths, saturated conductivity and sorptive number. The point source, groundwater table and soil surface are hydrologically intertwined, with formation of dividing surfaces (separatrices) and critical lines.",
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N2 - Flows in homogeneous topsoils with a subjacent substratum or horizontal groundwater table generated by line-point emitters are studied and tracked back to the Kornev method of subsurface irrigation. Laplace's equation governs flow in a saturated or tension-saturated hat-shaped zone subtended by the substratum, provided pressure in a porous pipe or mole hole is positive. For low capillarity a free surface (phreatic line or capillary fringe) and a layer-substratum interface of a constant vertical component of velocity bound the flow domain. The free surface is found for various values of source strengths, emitter elevation above the substratum and the ratio of hydraulic conductivities of the topsoil and substratum. Subcritical and supercritical regimes are distinguished. In the limit of an impermeable substratum, the Riesenkampf solution for a line source is analysed. In soils of high capillarity, the J.R. Philip model of a point source and 'exponential mirror principle' give a series solution for a vertical array of alternating sources and sinks. Four topological situations emerge, depending on the layer thicknesses, topsoil potential, source depths strengths, saturated conductivity and sorptive number. The point source, groundwater table and soil surface are hydrologically intertwined, with formation of dividing surfaces (separatrices) and critical lines.

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