Vector potential functions and stream surfaces in three-dimensional groundwater flow

Two new developments are reported in this dissertation. The first development regards stream surfaces of the specific discharge vector for divergence-free flows. An analytic expression is derived for the angle of intersection between two stream surfaces in a two-dimensional flow. It is shown that stream surfaces in a two-dimensional, non-uniform flow that are neither horizontal nor vertical may only intersect orthogonally at isolated points. This disproves an assumption that has been published by many researchers; they assume that stream surfaces that intersect orthogonally at one point will intersect orthogonally along the entire intersection of the two surfaces. It is also shown that there is a fundamental difference between stream surfaces in three-dimensional flows and in two-dimensional flows. A three-dimensional feature may change the shape of vertical cross sections through a stream tube, and these changes may be observed throughout the aquifer. A two-dimensional feature will only affect the shape of these cross sections locally.;The analytic elements presented in this dissertation were used to model capture zones for wells in a three-dimensional flow. The objective of this study was to determine the type of well that would capture a contaminated leachate with the minimum pumping rate. For the aquifer configuration that was studied, it was found the most efficient type of well is a horizontal well that is oriented perpendicularly to the direction of uniform flow.;The second development regards the vector potential function of the specific discharge vector for three-dimensional flows. Mathematical expressions are derived for the vector potential of elements that model partially penetrating wells, horizontal wells, and rectangular areas of infiltration. The vector potential is used to compute the discharge across a surface; this discharge is obtained by integrating the tangential component of the vector potential along the boundary of the surface. Closed form expressions of the resulting integrals are obtained for some of the elements; this integral is evaluated numerically for the other elements.