Beach water table fluctuations due to wave run-up: Capillarity effects

High-frequency beach water table fluctuations due to wave run-up and rundown have been observed in the field [Waddell, 1976]. Such fluctuations affect the infiltration/exfiltration process across the beach face and the interstitial oxygenation process in the beach ecosystem. Accurate representation of high-frequency water table fluctuations is of importance in the modeling of (1) the interaction between seawater and groundwater, more important, the effects on swash sediment transport and (2) the biological activities in the beach ecosystem. Capillarity effects provide a mechanism for high-frequency water table fluctuations. Previous modeling approaches adopted the assumption of saturated flow only and failed to predict the propagation of high-frequency fluctuations in the aquifer. In this paper we develop a modified kinematic boundary condition (kbc) for the water table which incorporates capillarity effects. The application of this kbc in a boundary element model enables the simulation of high-frequency water table fluctuations due to wave run-up. Numerical tests were carried out for a rectangular domain with small-amplitude oscillations; the behavior of water table responses was found to be similar to that predicted by an analytical solution based on the one-dimensional Boussinesq equation. The model was also applied to simulate the water table response to wave run-up on a doping beach. The results showed similar features of water table fluctuations observed in the field. In particular, these fluctuations are standing wave-like with the amplitude becoming increasingly damped inland. We conclude that the modified kbc presented here is a reasonable approximation of capillarity effects on beach water table fluctuations. However, further model validation is necessary before the model can confidently be used to simulate high-frequency water table fluctuations due to wave run-up.