Cylindrically Confined Flows of Water from a Point Source and to a Sink, above a Water Table

Abstract

A quasi‐linear form of Richards' equation, which assumes exponential dependence of the hydraulic conductivity on the pressure head and depth, was used to analyze the flows from a point source and to a point sink in a cylindrically confined soil domain overlying a shallow groundwater table (WT). The evaporation flux at the surface was taken to be proportional to the matric flux potential (MFP). Analytical solutions for the time‐dependent and steady‐state problems were obtained by using integral transforms. The general solution for a point source in a finite‐length cylinder takes the form of double series, which contains the inverse of the finite Hankel transform in the radial direction coupled with the inverse of the generalized Fourier transform in the vertical direction. Numerical evaluation of this solution is straightforward but time consuming for both time‐dependent and steady‐state cases. An alternative solution for a steady point source that involves only the Hankel inverse transform was found to be more practicable. Steady flows from a surface point source toward a WT and from a WT toward a subsurface sink were analyzed by mapping the distributions of the pressure head and the MFP, together with the streamlines. The sink was simulated by a suction zone of prescribed radius whose strength was evaluated from the condition that MFP equals zero at a reference point at either the bottom or the top of the suction zone. Particular attention was paid to the choice of locations of the reference point for evaluating the sink strength, for which the solution for the sink remains physically relevant irrespective of whether or not the surface loses water by evaporation.

Minimizing Evaporation by Optimal Layering of Topsoil: Revisiting Ovsinsky's Smart Mulching‐Tillage Technology Via Gardner‐Warrick's Unsaturated Analytical Model and HYDRUS

“…Now we assume that k ( Z ) = K 0 ( Z )exp[ α ( Ζ ) p ( Z )], where K 0 ( Z ) and α ( Z ) are two given functions. For simplicity, we assume that these two functions are correlated according to an empirical function from Communar and Friedman (): where K 0 ( Z ) is in cm/hr, α ( Z ) is in 1/cm, and C a is in h 1/2 /cm 3/2 . There are numerous pedotransfer functions and other empirical relations between K 0 ( Z ) and α ( Z ), which can be used instead of equation .…”

“…Now we assume that k(Z) = K 0 (Z)exp[α(Ζ) p(Z)], where K 0 (Z) and α(Z) are two given functions. For simplicity, we assume that these two functions are correlated according to an empirical function from Communar and Friedman (2015):…”

Analytical solution for tension‐saturated and unsaturated flow from wicking porous pipes in subsurface irrigation: The Kornev‐Philip legacies revisited

“…Nowadays, Kornev's engineering experience and agronomic achievements are left in oblivion. In the last four decades, the technical solutions enunciated in K‐35 were rediscovered in numerous works on subsurface irrigation [see, e.g., Ashrafi et al ., ; Akhoond‐Ali and Golabi , ; Communar and Friedman , ; El‐Nesr , ; Gupta et al ., ; Hosseinalipour and Aghakhani , ; Iwama et al ., ; Janani et al ., ; Kato and Tejima , ; Lazarovitch et al ., ; Moniruzzaman et al ., ; Patel and Rajput , ; Provenzano , ; Shani et al .,; Siyal and Skaggs , ; Siyal et al ., ; Tanigawa et al ., ; Thebaldi et al ., ; Warrick and Shani , ; Yabe and Tanigawa , ], unfortunately, without referencing the seminal Kornev publications.…”

Steady Water Flow with Interacting Point Source–Point Sink–Water Table in a Cylindrical Soil Domain

“…The presence of a WT at shallow depth can greatly affect the flow patterns in the overlying soil domain, as addressed, for example, by the analytical studies of Warrick and Lomen (1977), Philip (1989), Martinez and McTigue (1991), de Rooij et al (1996), and Basha (2000). Communar and Friedman (2015) derived an analytical solution for water flow from (or to) a surface (or subsurface) point source (or sink) in a confined cylindrical domain with a lower boundary consisting of a shallow WT of a prescribed pressure head and an upper boundary consisting of an evaporating soil surface. They also demonstrated the effects of WT depth, cylinder radius, and evaporation on flow patterns that arise under the action of either a single point source or point sink.…”

“…The analytical solution for the point source applied to the analysis (Communar and Friedman, 2015) uses Gardner's (1958) model, in which hydraulic conductivity is an exponential function of the pressure (matric) head, which enables linearization of Richards' equation for steady flow. In Communar and Friedman (2015), a general form was derived and presented that also accounts for evaporation from the soil surface and vertical variation of the soil hydraulic conductivity at saturation. In the following, it is presented in a reduced form for the case of no vertical flux at the soil surface and for a homogeneous soil profile.…”