Surface water impoundment in an unlined triangular ditch during a single managed aquifer recharge (MAR) infiltration pulse lasts for time Te, after which all initially disposed water seeps into a homogenous isotropic coarse soil. In ditches with initial water W0 with depth H0 and length L, the dyad (W0,H0) vanishes at t→Te. The ditch slope that minimizes an objective function involving a linear combination of Te, W0, and H0 with arbitrary cost coefficients was found. The analytical expression for Te as a function of the bank slope and the sand's porosity is for soils without capillarity and mild bank slopes. An isoperimetric constraint in optimization is the volume of the water pulse released into the ditch. A global unique minimum exists if the coefficients factoring W0 and H0 are not identically zero. A numerical solution to a two-dimensional infiltration problem was obtained using HYDRUS 2D/3D and its reservoir boundary condition option for arbitrary soils and bank slopes. Optimal slopes of triangular ditches were found for an initially dry loam. The analytical and numerical optimal shapes were not sensitive to mild variations of the ditch slope.
A transport model was developed to simulate the seawater intrusion in the aquifer system along the Kalbha and Fujairah coast of the United Arab Emirates. The model was used to simulate the salinity levels of the groundwater of Wadi Ham aquifer and its variation in time and space from January 1994 to March 2005. The area covering the coast of Gulf'of Oman in the study domain was taken as a constant concentration boundary with an average salinity (TDS) value of 35 000 mg/L. The effect of artificial recharge on seawater intrusion was evaluated. The results of the simulation indicated that the seawater intrusion is affected by the dry and wet conditions. During the dry years, the velocity vectors are directed from the Gulf of Oman to the aquifer causing severe intrusion problems. During the wet years when rainfall is relatively high and groundwater recharge is encountered from the ponding area of Wadi Ham dam, the velocity vectors are reversed.
Abstract The Dupuit‐Forchheimer (DF) approximation for unconfined groundwater flows is reduced to 2D Poisson's equation (PE), the right hand side of which involves an intensive evapotranspiration (ET) rate. A shallow water table dips inward from a constant piezometric head boundary (closed curve) such that a “dry gap,” demarcated by another closed curve (unknown front), may emerge. Apriori estimates of the volume of the saturated zone and of the “dry gap” area are important for water resources management in drylands. We use the results from the theory of linear elasticity, torsion of elastic bars, for which PE is solved for the Prandtl function. Using the Poincaré metrics with the Gaussian constant curvature , isoperimetric inequalities are obtained for steady‐state DF flows. Conformal moments and confromal radii of the domains and 2‐D Hardy's type inequalities in domains, modeling the Saint Venant bar torsion problem, are involved in the obtained estimates. The studied boundary value problems (BVPs) are nonlinear for ET rates depending on the depth of the water table. In the DF model, the vadose zone (VZ) is considered as a “distributed sink” (similar to a standard “distributed source,” which models recharge to the water table in humid climates). The analytical VZ is collated with one obtained from a numerical solution to BVP for Richards’ equation in a 3‐D saturated‐unsaturated flow. BVPs for Richards’ equation in cylindrical domains, solved by HYDRUS software, give the pressure head, moisture content, Darcian velocity fields, and streamlines.
Abstract Ovsinsky (1899, https://www.rulit.me/books/novaya‐sistema‐zemledeliya‐read‐193251‐1.html ) suggested and tested a water conserving soil no‐till technology for rain‐snow‐fed field crops in a semiarid environment in southern Russia. We model Ovsynsky's unsaturated flow fragment, in which 1‐D steady evaporation and evapotranspiration through a two‐layered soil from a horizontal static water table to a dry soil surface takes place. Gardner's exponential and algebraic functions are used for the unsaturated hydraulic conductivity‐suction head relations. The vertical evaporation flux depends on the dyads and triads (correspondingly) of the parameters of these functions, for example, the saturated hydraulic conductivity and the sorptive number of the two layers. The flux, as a function of the relative thickness of the upper stratum, is analytically found from the solution of one or two nonlinear equations. This relation can be nonmonotonic and exhibits either a minimum or maximum depending on whether this stratum is coarser or finer than the subjacent stratum fed from a horizontal isobar. HYDRUS‐1D simulations confirm these extrema. This explains the experimental results from the literature on mulching/tillage/soil crusting‐sealing, which can increase, decrease, or have no impact on evaporation from a shallow water table. Alterations of the soil's homogeneity to reduce evaporation losses can improve the hydrological balance of soil profiles.
