The known formulae of Freeze and Cherry, Polubarinova–Kochina, Vedernikov for flow rate during 2-D seepage into horizontal drains and axisymmetric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of drain depth providing minimal seepage rate is presented. The depth is found exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bottom is analysed and the difference in rate as compared with a completely filled cavity is established. Rate values for slot drains in a two-layer aquifer are 'inverted' using the Schulgasser theorem from the Polubarinova–Kochina expressions for corresponding flow rates under a dam. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated flow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities are addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restriction. © 1998 John Wiley & Sons, Ltd.
A pedological study of the reservoir bed of Al-Khoud Dam, Oman, revealed an unusual sedimentation pattern which evolved into an intricate composition of silt blocks surrounded by vertical cracks and horizontal layers filled with a "proppant" sand. The discovered soil morphology reflects the complex topology of water motion (infiltration–seepage–evaporation) through the sand-filled cracks/layers and blocks during both the rare flood events and ensuing periods of ponding, and the long, intervening dry periods. These naturally formed soils demonstrate an ability to preserve a large quantity of water inside the silty blocks at depths of 0.5 to 1.5 m, despite the high temperature and dryness of the topsoil. The hydrological optimality and "smartness" of these soils is attributed to the unique block-crack system. Natural, lush vegetation was found in adjacent zones of the reservoir bed, and acted as a footprint of the shallow "fractured perched aquifer". Planted "ivy" (Convolvulaceae) in the vertical face of one pedon showed intensive growth without irrigation. Soil moisture content data confirmed the hydrological immobility of water in the blocks if not depleted by transpiration. The novel phenomena reported unveil the possible alteration of soil heterogeneity for optimization of the soil–water system in arid zone soils.
Soil moisture content is a critical factor in the hydrological cycles of terrestrial ecosystems, especially in sandy environments. The spatial variation in soil water content is influenced by both dynamic and static factors. To understand the ecohydrology of desert environments, a detailed analysis of the vadose zone and topsoil in coastal dunes is essential. This study focuses on the soil hydrology of coastal mini-dunes (Nabkhas) in the Al-Hail North area of Oman, particularly examining moisture redistribution following a 13 mm rainfall event. The area, characterized by a sabkha landform with a shallow water table (approximately 1.4 meters below the surface), is interspersed by an array of Nabkhas. The length and height of three Nabkhas (N1, N2, and N3) were measured. Native plants were present in all Nabkhas: Haloxylon salicornicum in N1 (alive) and N3 (dead), and Salvadora persica in N2. Soil samples were collected from the interdune and Nabkha cores for grain size analysis. Decagon EC-05 sensors were installed at depths of 0 and 20 cm in the vertical profiles of N1, N2, and N3 to monitor diurnal variations in volumetric water content (ϴv).A significant increase in ϴv in the top sensor immediately after the rain event was detected, while the bottom sensor showed a minimal increase over time. The top sensor's ϴv peaked at 0.1 m³/m³ on the last day of the rain event, then decreased to 0.054 m³/m³ after 8 days due to evaporation. The bottom sensor's ϴv reached a maximum of 0.58 m³/m³ on the final recording day. The spatial and temporal variation in ϴv is also influenced by vapor condensation from humid air and around native shrubs. High moisture content in the top layers of dunes significantly impacts vegetation patterns.Another field investigation examined soil moisture variability using excavated profiles at four locations, including three sites under Nabkhas and a vegetation-free control plot. Analysis of volumetric water content demonstrated clear moisture stratification throughout the profiles. Near-surface soil layers showed minimal moisture levels, consistent with the residual water content (θr) typical in desert sandy soils. Moving downward through the profile, a significant increase in moisture content was detected, with lower horizons reaching near-saturation conditions (θs). This enhanced water retention in deeper layers was associated with both finer soil textures and water table influence. Such moisture-rich deeper soil zones appear to provide continuous capillary water movement to Nabkha vegetation root systems, enabling water redistribution throughout the soil-vegetation-atmosphere interface.This study contributes to the conservation/restoration of desert vegetation and understanding the resilience of small-scale soil-water-plant ecosystems in arid regions. Further research on soil properties, water availability, and microclimate close to Nabkhas is necessary better to comprehend plant distribution and functioning in these landforms. 
: The ultimately stable slopes in the cases of seepage through the earth dam, under the sheet piling, and to the drainage trench are founded by the methods of linear differential equations, boundary-value problems, and hodograph of velocity. INTRODUCTION 1, A STABLE SLOPE OF AN EARTH DAM 2. A STABLE BOUNDARY OF A DOWNSTREAM SLOPE 3. A STABLE PROFILE OF A DRAINAGE TRENCH RESULTS REFERENCES
Abstract The authors solve the problems of controlling the shape of hydraulic structures (apron, channel, drain, earth dam) under the condition of the extremum of integral seepage characteristics. The extremals and the corresponding estimates are found by the method of inverse boundary‐value problems within the scope of the theory of analytical functions.
The Bystrov explicit analytical solution for viscous, low‐Reynolds number flow in layers of variable thickness is interpreted as infiltration in a Gardner homogeneous soil obstructed by a subterranean cavity, stone, or other obstacle. Mathematically, the two‐dimensional advection–dispersion equation for the Kirchhoff potential is solved by combination of a term responsible for incident unidirectional infiltration, and a term describing a dipole. Superposition results in a separatrix (a cavity or stone contour), outside of which streamlines are deflected from vertical lines, and constant potential (pressure, moisture content) lines demarcating lobe‐shaped domains. The physical impedance of the obstacle causes a buildup of moisture near the leading edge and a dry zone near the trailing edge of the obstacle. The criticality conditions of the model were also tested (i.e., that the moisture content in the flow domain is less than porosity but greater than zero).
For the Boussinesq and Charny nonlinear diffusion equations we employ the known similarity solutions and derive new ones using the Adomian decomposition method and separation of variables. For a periodic water-drive regime with a heavier fluid sweeping a lighter one from a porous formation we arrive at an explicit analytical expression for the interface and describe the phenomena of “superpropagation” and “counterslumping” that date back to tidal “superelevation” in coastal unconfined aquifers described by J.R. Philip. Similarly, for a two-phase flow with a straight sharp interface separating two fluids of contrasting viscosity the interface in a periodic drive regime propagates deeper than in a constant rate sweep. Applications to groundwater hydrology and petroleum engineering are discussed.
Abstract Macroscopically, a Darcian unsaturated moisture flow in the top soil is usually represented by an one-dimensional volume scale of evaporation from a static water table. On the microscale, simple pore-level models posit bundles of small-radius capillary tubes of a constant circular cross-section, fully occupied by mobile water moving in the Hagen–Poiseuille (HP) regime, while large-diameter pores are occupied by stagnant air. In our paper, cross-sections of cylindrical pores are polygonal. Steady, laminar, fully developed two-dimensional flows of Newtonian water in prismatic conduits, driven by a constant pressure gradient along a pore gradient, are more complex than the HP formula; this is based on the fact that the pores are only partially occupied by water and immobile air. The Poisson equation in a circular tetragon, with no-slip or mixed (no-shear-stress) boundary conditions on the two adjacent pore walls and two menisci, is solved by the methods of complex analysis. The velocity distribution is obtained via the Keldysh–Sedov type of singular integrals, and the flow rate is evaluated for several sets of meniscus radii by integrating the velocity over the corresponding tetragons.
An explicit closed-form analytical solution giving the water-table depression is obtained for the steady-state problem of seepage to a water-bearing substratum from two reservoirs separated by a strip of land over which water loss by evaporation occurs at a constant rate. Two hydrodynamic situations can occur. In the first, there is only drainage into the substratum and all evaporating water originates from the reservoirs. In the second, the substratum, while accepting water draining from the reservoirs, also supplies some water to the evaporating surface. The method of boundary-value problems is used through the conformal mapping of a strip in the Zhukovskii plane to an auxiliary half-plane and reconstruction of the complex physical coordinate by the Signorini formula. The two hydrodynamic regimes are demarcated in the solution with the shape of the water table obtained in a closed form. The results of calculations show the effect of the evaporation rate, the hydraulic conductivity of the soil, the pressure in the water-bearing substratum, the distance between reservoirs, and the depth to the substratum. The method of boundary-value problems is also used to obtain an analytical solution for the water-table depression caused by evaporation from a strip in an infinite extent of land above a water-bearing substratum under pressure.
