Abstract 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.

中文翻译：

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饱和和不饱和土壤中的沟渠渗流和地形洼地

摘要 由线汇或点汇排干封闭半无限含水层所产生的等压线是一条解析曲线，稳定的二维平面或轴对称达西流向其收敛。这个水槽可能代表地球上的挖掘、沟渠或干河，或火星上的渠道。下沉的强度控制着沟渠凹陷的形式：对于二维流动，等压线的形状从零深度通道变为半圆形；对于轴对称流动，可以重建像圆盘一样平坦或像半球一样深的凹陷。在轴对称流模型中，一个虚构的 JR 菲利普点水槽由无数个水槽和水源阵列镜像，这些水槽和水源沿着垂直于水平地下水位的垂直线放置。地形洼地保持恒定的毛细管压力（含水量，基尔霍夫电位）。这些奇点都不属于真正的流动域，蒸发不饱和加德纳土壤。流向三角形、空的或部分填充的沟渠的饱和流通过保形映射和参考平面中的黎曼问题的解决方案来解决。获得的渗流流速用作柯西问题 ODE 的右手边，该问题的解给出了绘制曲线，即初始空槽中水位的上升。饱和和非饱和土壤中流动的 HYDRUS-2D 计算与解析解很好地匹配。建模结果应用于地球上真实水文通量的评估和火星水文地貌的古重建。空的或部分填充的沟渠通过共形映射和参考平面中的黎曼问题的解决方案来解决。获得的渗流流速用作柯西问题 ODE 的右手边，该问题的解给出了绘制曲线，即初始空槽中水位的上升。饱和和非饱和土壤中流动的 HYDRUS-2D 计算与解析解很好地匹配。建模结果应用于地球上真实水文通量的评估和火星水文地貌的古重建。空的或部分填充的沟渠通过共形映射和参考平面中的黎曼问题的解决方案来解决。获得的渗流流速用作柯西问题 ODE 的右手边，该问题的解给出了绘制曲线，即初始空槽中水位的上升。饱和和非饱和土壤中流动的 HYDRUS-2D 计算与解析解很好地匹配。建模结果应用于地球上真实水文通量的评估和火星水文地貌的古重建。在最初空的沟渠中水位上升。饱和和非饱和土壤中流动的 HYDRUS-2D 计算与解析解很好地匹配。建模结果应用于地球上真实水文通量的评估和火星水文地貌的古重建。在最初空的沟渠中水位上升。饱和和非饱和土壤中流动的 HYDRUS-2D 计算与解析解很好地匹配。建模结果应用于地球上真实水文通量的评估和火星水文地貌的古重建。