TY - JOUR

T1 - Seepage to ditches and topographic depressions in saturated and unsaturated soils

AU - Kacimov, A. R.

AU - Obnosov, Yu V.

AU - Šimůnek, J.

N1 - Funding Information:
This work was supported bySultan Qaboos University via the grant “Rise of Water-table and Its Mitigation at SQU Campus”, grant DR\RG\17 and it was carried out as part of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District, agreement No. 075-02-2020-1478. Helpful comments by two anonymous referees are highly appreciated.
Funding Information:
This work was supported bySultan Qaboos University via the grant ?Rise of Water-table and Its Mitigation at SQU Campus?, grant DR\RG\17 and it was carried out as part of the development program of the Scientific and Educational Mathematical Center of the Volga Federal District, agreement No. 075-02-2020-1478. Helpful comments by two anonymous referees are highly appreciated.
Publisher Copyright:
© 2020 Elsevier Ltd

PY - 2020/11

Y1 - 2020/11

N2 - An isobar generated by a line or point sink draining a confined semi-infinite aquifer is an analytic curve, to which a steady 2-D plane or axisymmetric Darcian flow converges. This sink may represent an excavation, ditch, or wadi on Earth, or a channel on Mars. The strength of the sink controls the form of the ditch depression: for 2-D flow, the shape of the isobar varies from a zero-depth channel to a semicircle; for axisymmetric flow, depressions as flat as a disk or as deep as a hemisphere are reconstructed. In the model of axisymmetric flow, a fictitious J.R. Philip's point sink is mirrored by an infinite array of sinks and sources placed along a vertical line perpendicular to a horizontal water table. A topographic depression is kept at constant capillary pressure (water content, Kirchhoff potential). None of these singularities belongs to the real flow domain, evaporating unsaturated Gardnerian soil. Saturated flow towards a triangular, empty or partially-filled ditch is tackled by conformal mappings and the solution of Riemann's problem in a reference plane. The obtained seepage flow rate is used as a right-hand side in an ODE of a Cauchy problem, the solution of which gives the draw-up curves, i.e., the rise of the water level in an initially empty trench. HYDRUS-2D computations for flows in saturated and unsaturated soils match well the analytical solutions. The modeling results are applied to assessments of real hydrological fluxes on Earth and paleo-reconstructions of Martian hydrology-geomorphology.

AB - An isobar generated by a line or point sink draining a confined semi-infinite aquifer is an analytic curve, to which a steady 2-D plane or axisymmetric Darcian flow converges. This sink may represent an excavation, ditch, or wadi on Earth, or a channel on Mars. The strength of the sink controls the form of the ditch depression: for 2-D flow, the shape of the isobar varies from a zero-depth channel to a semicircle; for axisymmetric flow, depressions as flat as a disk or as deep as a hemisphere are reconstructed. In the model of axisymmetric flow, a fictitious J.R. Philip's point sink is mirrored by an infinite array of sinks and sources placed along a vertical line perpendicular to a horizontal water table. A topographic depression is kept at constant capillary pressure (water content, Kirchhoff potential). None of these singularities belongs to the real flow domain, evaporating unsaturated Gardnerian soil. Saturated flow towards a triangular, empty or partially-filled ditch is tackled by conformal mappings and the solution of Riemann's problem in a reference plane. The obtained seepage flow rate is used as a right-hand side in an ODE of a Cauchy problem, the solution of which gives the draw-up curves, i.e., the rise of the water level in an initially empty trench. HYDRUS-2D computations for flows in saturated and unsaturated soils match well the analytical solutions. The modeling results are applied to assessments of real hydrological fluxes on Earth and paleo-reconstructions of Martian hydrology-geomorphology.

KW - Analytic and HYDRUS solutions for Darcian 2-D and axisymmetric flows in saturated and unsaturated soils towards drainage ditches and topographic depressions

KW - Boundary value problems involving seepage faces on Earth and Mars

KW - Complex potential and conformal mappings

KW - Evaporation and seepage exfiltration from shallow groundwater

KW - Isobars, isotachs, constant piezometric head, and Kirchhoff potential lines

KW - Method of images with sinks and sources for the Laplace equation and ADE

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U2 - 10.1016/j.advwatres.2020.103732

DO - 10.1016/j.advwatres.2020.103732

M3 - Article

AN - SCOPUS:85089935842

VL - 145

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

M1 - 103732

ER -