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 solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection–diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring–neap tides (a bichromatic tidal system with the fundamental frequencies ω₁andω₂) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency ω₁−ω₂, i.e., the spring–neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations.