Boussinesq's Equation Solutions for Semi‐Infinite Aquifer

Abstract

The problem of unsteady flow in an unconfined semi-infinite aquifer adjacent to a surface reservoir, both resting on an horizontal impervious stratum, for the conditions of instantaneous lowering of the free water surface in the reservoir from H to d, is examined in detail, on the basis of the well known Boussineq's one dimensional nonlinear differential equation describing the flow. Three linearization methods are reviewed and the expressions concerning the water table level, h, and the discharge at the exit section, Q, are given. In all linearization methods the basic assumption is that the water table height h varies little from a mean value h¯. Numerical results of all approximate analytical solutions depend strongly on the selected value of h¯. A systematic numerical solution of the nonlinear Boussinesq's differential equation for the same problem was presented by Yeh in 1970. Comparing the results of the three approximate solutions, each one with four different choices of h¯, with the numerical results of Yeh, a semi-empirical expression of h¯ is defined, which in conjunction with the second solution gives excellent results.