Groundwater flow due to a nonlinear wave set-up on a permeable beach

Water flow through the beach body plays an important role in the biological status of the organisms inhabiting the beach sand. For tideless seas, the groundwater flow in shallow water is governed entirely by the surface wave dynamics on the beach. As waves propagate towards the shore, they become steeper owing to the decreasing water depth and at some depth, the waves lose their stability and start to break. When waves break, their energy is dissipated and the spatial changes of the radiation stress give rise to changes in the mean sea level, known as the set-up. The mean shore pressure gradient due to the wave set-up drives the groundwater circulation within the beach zone. This paper discusses the circulation of groundwater resulting from a nonlinear set-up. The circulation of flow is compared with the classic Longuet-Higgins (1983) solution and the time series of the set-up is considered for a 24 h storm. Water infiltrates into the coastal aquifer on the upper part of the beach near the maximum run-up and exfiltration occurs on the lower part of the beach face near the breaking point.