Water-table response to tidal forcing at sloping beaches

The groundwater response to tidal forcing is described by Laplace's equation for the hydraulic head subject to appropriate boundary conditions. A previous solution to this problem based on long-wave and shallow-aquifer approximations is extended to higher-order and a general solution scheme, automated in Mathematica, is described. The solution can, in principle, be extended to arbitrary order, but is restricted to a detailed study of the properties of the solution when truncated to sixth-order. These results show that the mean water table height increases throughout the aquifer to a steady inland height elevated above mean sea level. The phase shift of the fluctuations and the asymmetry of the pore drainage process are investigated using Fourier analysis.