Mathematical Model for Beach Groundwater Fluctuations

The measurement of changing water levels across a tropical carbonate beach profile over three tidal cycles has provided basic data for the development of a predictive mathematical model of the fluctuation in the level of a beach water table. The model is based on partial differential equations governing transient, one‐dimensional movement of groundwater through porous media. A finite difference algorithm for the digital computer was developed to solve the equations. Beach homogeneity and nonlinear boundary conditions imposed by tidal fluctuations were assumed in these calculations. Field measurements of water table fluctuations in Galleon Beach, Grand Cayman Island, show that the mathematical model simulates this system within the limits of accuracy of the experimental measurements. A method for in situ determination of the permeability‐porosity ratio is proposed and demonstrated for the beach studied. The mathematical model of the beach water table is used to develop an accurate method of calculating inflow and outflow at the beach‐ocean interface.