Analytic solutions for quasi-3D seepage in a shallow unconfined aquifer as a plane composed of a transpiration-inducing park and its hydraulically commingled exterior

Strack's (1984, 2017) analysis of infiltration from a pond into a shallow aquifer, with a generated groundwater mound, is modified for steady phreatic groundwater flows in perched aquifers, typical for arid/hyperarid environments, with a zone of intensive transpiration and induced groundwater trough. The interior of an urban phreatophytic park is an n-polygon (in an aerial view), which degenerates into a circle at n→∞. Transpiration acts as an areal groundwater sink. The water table drawdown is hydrologically symmetric with Strack's drawup. In the exterior of the park, the ground surface is phyto-sterile (e.g. a desert in Arabia or a paved megapolis) and evapotranspiration from the water table there is ignored. The travel (residence) time of advected marked particles along the flowpaths (streamlines) towards the park and under it are analytically evaluated. In terms of the Dupuit-Forchheimer model of a vertically averaged hydraulic head, the Strack potential obeys the Laplace and Poisson equations in polygon's exterior and interior (correspondingly), with a hydraulic commingling along the park boundary. The tracer particles start their topologically converging journey from a remote circular zone of contamination (e.g. sewage from urban septic tanks recharging the water table). Porosity, hydraulic conductivity of the aquifer, evapotranspiration rate and a piezometric head in a remote observational well are given. For a circular park flow is 1-D radial. In the park exterior, the Schwarz-Christoffel formula maps conformally the physical domain (an infinite trigon) onto a half-strip in the complex potential plane. Strack's potential is expressed via hypergeometric functions, whose parameters depend on n. The flow net is reconstructed with the help of the stream function. For a triangular park interior, there is no stream function and the Saint-Venant solution to the Poisson equation is engaged to find the water table, hydraulic gradients, and discharge streamlines. The total dewatered volume and groundwater storage under the water table and “gross travel time” are evaluated for circular parks. Implications for ecohydrology of parks and desert oases in the Gulf countries and intuitive isoperimetric problems are discussed.