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

Abstract

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, ε N = αεcot β (in which β is the beach slope, α is the amplitude parameter and ε is the shallow water parameter) and are limited to tan −1( αε)≪ β⩽ π/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 ε and α increase, and reaches 7% of the linear solution.