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

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, <f>&epsiv;N=α&epsiv;cotβ</f> (in which <f>β</f> is the beach slope, <f>α</f> is the amplitude parameter and <f>&epsiv;</f> is the shallow water parameter) and are limited to <f>tan−1(α&epsiv;)≪β&les;π/2</f>. 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 <f>&epsiv;</f> and <f>α</f> increase, and reaches 7% of the linear solution. [Copyright &y& Elsevier]