A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

NOTE: THE MATHEMATICAL SYMBOLS IN THIS ABSTRACT CANNOT BE DISPLAYED CORRECTLY ON THIS PAGE. PLEASE REFER TO THE ABSTRACT ON THE PUBLISHER'S WEBSITE FOR AN ACCURATE DISPLAY. The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, N=acotß (in which ß is the beach slope, a is the amplitude parameter and is the shallow water parameter) and are limited to tan-1(a)ßp/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as and a increase, and reaches 7% of the linear solution.