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 - 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

UR - http://www.scopus.com/inward/record.url?scp=85089935842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089935842&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2020.103732

DO - 10.1016/j.advwatres.2020.103732

M3 - Article

AN - SCOPUS:85089935842

SN - 0309-1708

VL - 145

JO - Advances in Water Resources

JF - Advances in Water Resources

M1 - 103732

ER -