Analytic Solutions for Infiltration-Evaporation Formed Fresh Groundwater Lenses Floating on Saline Water Table Under Desert Dunes: Kunin-Van Der Veer Legacy Revisited

Explicit expressions for the vector fields of specific discharge and scalar fields of stream functions and piezometric heads in a Darcian steady-state essentially two-dimensional (2-D) flow through a three-component composite representing a vertical or horizontal well with a gravel pack and annular skin are obtained and analysed. The refraction conditions along two concentric circles, which represent interfaces between three porous media of contrasting hydraulic conductivities, are exactly satisfied. Flow nets, isotachs, the locus of the stagnation point bounding the capture zone of the well, and functionals quantifying area-averaged hydraulic characteristics are found. The flow topology and drawdowns near the well illustrate that at small pumping rates a common concept of a purely radial 1-D flow can be superficially plausible but misleading.1-1

Size and Shape of Steady Seawater Intrusion, Sharp-Interface Wedge: the Polubarinova-Kochina Analytical Solution to the Dam Problem Revisited

Путем перемасштабирования геометрических размеров и величины гидравлической проводимости в классической задаче двумерного потенциального течения через прямоугольную земляную перемычку с пустым нижним бьефом показано, что это дает математически эквивалентную задачу о вторжения морской воды с резкой границей раздела пресных грунтовых и соленых морских вод. Горизонтальный водоносный горизонт разгружается в море через вертикальный отрезок пляжа. Форма границы раздела вод, вертикальные, горизонтальные размеры статического языка и его площадь поперечного сечения записаны в явном виде, используя исправленные формулы Полубариновой-Кочиной. Плотности двух жидкостей, коэффициент фильтрации и толщина пласта, а также бытовой гидравлический градиент служат в качестве входных параметров модели. С уменьшением градиента (например, связанного с откачками и водозабором из скважин) размеры клина быстро увеличиваются

Evaporation Induced Capillary Siphoning Through Hydraulically Connected Porous Domains: the Vedernokov-Bouwer Model Revisited

Evaporation-driven wicking of soil water through porous domains with contrasting hydraulic properties is studied analytically by conformal mappings and compared to numerical solutions. Initially, the connected rectangular domains are fully saturated. The first rectangle, Gp, is comprised of a coarse-textured porous medium with large permeability and low capillary forces. Evaporation-induced capillary flow pulls water horizontally across the domains to the surface of fine-textured rectangular domain, Gz, through an interfacial hydraulic exchange region that shrinks with time. The flow field in Gz is 2-D and is analytically expressed by the Vedernikov-Bouwer model that assumes a constant hydraulic conductivity for pressure heads higher than the air-entry value. The rate of 1-D drop of the phreatic surface in Gp is proportional to the evaporation rate (decreasing with time) from the Gz surface. The complex potential domain Gw "shrinks" with time, and at any time instance, it is conformally mapped onto Gz via two auxiliary planes using the Schwarz-Christoffel and Mobius transformations. The resulting Cauchy problem for an integro-differential equation with respect to an affix of the conformal mapping is solved using numerical algebra routines. A similar capillary coupled flow problem was numerically simulated using HYDRUS2D considering 2-D flow in both Gp and Gz. New insights into process dynamics are gained from a solution of an auxiliary optimization for a vertical imbibition in a column brought in contact with a water table where particle size (linking capillarity and permeability) is used as a control variable and counter-gravity front propagation dynamics as criteria.1-2

Modelign of seepage through embankments of earth-filled recharge dams in Oman: steady and transient regimes

Аналитически исследована линейная фильтрация через ядро плотины и примыкающие к нему сильнопористые присыпки. Течение в ядре анализируется с помощью конформного отображения пентагона в области годографа скорости на треугольник в физической плоскости

Control of Topology of Water Fluxes in Arid Agriculture: Amalgamation of Subsurface Irrigation, Managed Aquifer Recharge and Engineered Soil Substrat

We present the results of field-, farm- observations and experiments, as well as mathematical modeling of optimal control of descending, ascending and lateral water fluxes (viz., evapotranspiration, infiltration, seepage from/to subsurface emitters/drains, losses/gains from/to a deeper confined aquifer commingled via a leaky layer with the irrigated one, and water uptake by roots)

Profiling Ponded Soil Surface in Saturated Seepage Into Drain-Line Sink: Kalashnikov's Method of Lateral Leaching Revisited

Two boundary value problems are solved for potential steady-state 2-D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled with the aim of "uniformization" the velocity and travel time between this surface and a horizontal drain modelled by the sink. The complex potential domain is a half-strip, which is mapped onto a reference plane. Either the velocity magnitude or a vertical coordinate along the land surface are control variables. Either a complexified velocity or complex physical coordinate are reconstructed by solving mixed problems with the help of the Keldysh-Sedov formula via singular integrals, the kernel of which are the control functions. The flow nets, isotachs, and breakthrough curves are found by computer algebra routines. A designed soil hump above the drain ameliorates an unwanted "preferential flow" (shortcut) and improves leaching of salinized soil of a cropfield during a pre-cultivation season.1-1

Size and Shape of Steady Seawater Intrusion, Sharp-Interface Wedge: the Polubarinova-Kochina Analytical Solution to the Dam Problem Revisited

Путем перемасштабирования геометрических размеров и величины гидравлической проводимости в классической задаче двумерного потенциального течения через прямоугольную земляную перемычку с пустым нижним бьефом показано, что это дает математически эквивалентную задачу о вторжения морской воды с резкой границей раздела пресных грунтовых и соленых морских вод. Горизонтальный водоносный горизонт разгружается в море через вертикальный отрезок пляжа. Форма границы раздела вод, вертикальные, горизонтальные размеры статического языка и его площадь поперечного сечения записаны в явном виде, используя исправленные формулы Полубариновой-Кочиной. Плотности двух жидкостей, коэффициент фильтрации и толщина пласта, а также бытовой гидравлический градиент служат в качестве входных параметров модели. С уменьшением градиента (например, связанного с откачками и водозабором из скважин) размеры клина быстро увеличиваются

Dipolic MAR "bubble" inside confined brine formation or floating "lens" on top of unconfined saline aquifer.

333-340In arid desert environments, MAR sites are often characterized by high salinity of the ambient groundwater and intensive evaporation. We present mathematical modeling of two MAR scenarios: 1) injection-abstraction of fresh water through two horizontal wells with a quasi-vertical sharp interface/transition zone straddling between the caprock and bedrock of a confined aquifer; 2) infiltration from a surface pond into a floating fresh water lens with an interface pinned to two unknown frontal points. Analytical solutions for Darcian, steady, 2-D and axisymmetric flows utilize two types of mathematical dipoles: combination of a line sink and source and superposition of a distributed sink and source. For 2-D dipoles sandwiched between the caprock and bedrock, the theory of holomorphic functions is used (conformal mappings and Keldysh-Sedov's representations of characteristic functions via singular integrals). Numerically, MODFLOW-SEAWAT delineate isoconcentric lines of the MAR "bubble". For axisymmetric floating lenses, U-turn topology of fresh water circulation is modeled by the Dupuit-Forchheimer approximation, which is reduced to a boundary value problem for a nonlinear ordinary differential equation with respect to Strack's potential. The total volume of the lens is evaluated for evaporation rates, which are constant or exponentially decrease with the water table depth

Dipolic MAR "bubble" inside confined brine formation or floating "lens" on top of unconfined saline aquifer.

333-340In arid desert environments, MAR sites are often characterized by high salinity of the ambient groundwater and intensive evaporation. We present mathematical modeling of two MAR scenarios: 1) injection-abstraction of fresh water through two horizontal wells with a quasi-vertical sharp interface/transition zone straddling between the caprock and bedrock of a confined aquifer; 2) infiltration from a surface pond into a floating fresh water lens with an interface pinned to two unknown frontal points. Analytical solutions for Darcian, steady, 2-D and axisymmetric flows utilize two types of mathematical dipoles: combination of a line sink and source and superposition of a distributed sink and source. For 2-D dipoles sandwiched between the caprock and bedrock, the theory of holomorphic functions is used (conformal mappings and Keldysh-Sedov's representations of characteristic functions via singular integrals). Numerically, MODFLOW-SEAWAT delineate isoconcentric lines of the MAR "bubble". For axisymmetric floating lenses, U-turn topology of fresh water circulation is modeled by the Dupuit-Forchheimer approximation, which is reduced to a boundary value problem for a nonlinear ordinary differential equation with respect to Strack's potential. The total volume of the lens is evaluated for evaporation rates, which are constant or exponentially decrease with the water table depth

Seepage to Ditches and Topographic Depressions in Saturated and Unsaturated Soils

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-geomorphology1-1