A solution of the pattern of fresh-water flow in an unconfined coastal aquifer

Abstract

Fresh-water steady flow in an unconfined coastal aquifer satisfies Laplace's equations in a domain, two of whose boundaries are free surfaces, the upper boundary being the interface between air and fresh water and the lower boundary being the interface between fresh water and salt water. A method of solution based on observations of the governing equation and boundary conditions in the complex potential plane is used. Solution of the two-free-surface problem is presented in a dimensionless form. The validity of the method of solution is tested by applying it to the problem of fresh-water pattern in a confined coastal aquifer which is a problem with a single free surface. The solution of the single-free-surface problem obtained by the present method agrees exactly with that published by others. Comparisons of the two problems confirm that the solution of the problem in a confined aquifer can be used satisfactorily for practical purposes as an approximate solution to the problem in an unconfined aquifer. If the ratio of specific weight of salt water to that of fresh water is assumed to be 1.025, the upper free surface is in error by an amount less than 1.3%; the lower free surface and the outflow face are in error by less than 2.6%.