### 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 language | English |
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Journal | Irrigation and Drainage |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

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### 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

**Steady Darcian Flow in Subsurface Irrigation of Topsoil Impeded by a Substratum : Kornev-Riesenkampf-Philip Legacies Revisited.** / Obnosov, Yu V.; Kacimov, A. R.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Steady Darcian Flow in Subsurface Irrigation of Topsoil Impeded by a Substratum

T2 - Kornev-Riesenkampf-Philip Legacies Revisited

AU - Obnosov, Yu V.

AU - Kacimov, A. R.

PY - 2018/1/1

Y1 - 2018/1/1

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.

AB - 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.

KW - Advective-dispersion equation

KW - Emitter

KW - Kirchhoff potential

KW - Laplace's equation

KW - Method of images

KW - Water productivity

KW - Water productivity

UR - http://www.scopus.com/inward/record.url?scp=85041607643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041607643&partnerID=8YFLogxK

U2 - 10.1002/ird.2220

DO - 10.1002/ird.2220

M3 - Article

AN - SCOPUS:85041607643

JO - Irrigation and Drainage

JF - Irrigation and Drainage

SN - 1531-0353

ER -