A theoretical analysis of seepage flow of the confined groundwater into the lake bottom with a gentle slope

Abstract

Recently, in Japan, a new interest has been shown to the specific discharge of groundwater from the lake bottom in order to elucidate its influence on the quality and quantity of lake water. Using conformal mapping techniques, the authors describe analytically the steady two‐dimensional groundwater flow in an idealized confined aquifer, which extends infinitely with uniform thickness and constant inclination and is exposed to the lake bottom surface with a gentle slope. The techniques enable analytical calculation of the head and stream functions of groundwater in the aquifer and also the distribution of specific discharge at lake bottom surface. From the results of calculation, it is found that most of the aquifer water flows into the lake through the upper part of the surface of contact between lake and aquifer. This analysis may be useful in the evaluation of the role of groundwater seepage in the water balance of large lakes.

A Multiscale Investigation of Ground Water Flow at Clear Lake, Iowa

“…Other studies have shown the opposite or no trend (Woessner and Sullivan 1984;Belanger and Mikutel 1985;Krabbenhoft and Anderson 1986). Numerical analyses have also shown that discharge is concentrated near the shoreline (McBride and Pfannkuch 1975; Fukuo and Kaihotsu 1988). As an alternative to the method of Belanger and Kirkner (1994), ground water inflow was estimated using the adjusted median-specific discharge value and applying it to a percentage of the lake area near the shoreline.…”

Experimental Evaluation of Kovács’ Equations for Estimating Critical Gradients

“…As shown by the flownet for a submerged slope in Figure 4, the flow lines concentrate towards the top of the slope. Fukuo and Kaihotsu (1988) and van Beek et al 2014both derived analytical solutions for the distribution of exit gradient along the slope. As shown in Figure 5, the gradient changes exponentially near the top of the slope.…”

An Effect of Seiche on Groundwater Seepage Rate into Lake Biwa, Japan

“…In addition to these, stable isotope tracers [International Atomic Energy Agency, 1979; Krabbenhoft and Anderson, 1986;Krabbenhoft et al, 1990;Shimada et al, 1993], natural solutes [Stauffer, 1985], and analysis of the thermal regime [Andrews and Anderson, 1979;Lapham, 1989;Taniguchi, 1993] have been used for studies on interactions between surface and subsurface waters. An analytical study [Fukuo and Kaihotsu, 1988] and numerical studies [Winter, 1986;Anderson and Cheng, 1993;Cheng and Anderson, 1993;Nield et al, 1994] on the interaction between surface and subsurface waters have also been done. Fukuo and Kaihotsu [1988] theoretically analyzed seepage flow into a lake with a gentle slope by using conformal mapping techniques and found that most of the groundwater flows into the lake through nearsurface interface between lake and aquifer.…”

“…An analytical study [Fukuo and Kaihotsu, 1988] and numerical studies [Winter, 1986;Anderson and Cheng, 1993;Cheng and Anderson, 1993;Nield et al, 1994] on the interaction between surface and subsurface waters have also been done. Fukuo and Kaihotsu [1988] theoretically analyzed seepage flow into a lake with a gentle slope by using conformal mapping techniques and found that most of the groundwater flows into the lake through nearsurface interface between lake and aquifer. This was also found by McBride and Pfannkuch [1975].…”