Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutio ns to even the linearised Boussinesq equation. This paper presents a new pe rturbation approach to the problem that maintains the simplicity of the lin earised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an os cillating velocity. The perturbation method is applied to the propagation o f spring-neap tides (a bichromatic tidal system with the fundamental freque ncies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the t wo primary tidal oscillations, generating a slowly damped water table fluct uation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent wi th recently published field observations. (C) 2000 Elsevier Science Ltd. Al l rights reserved.