Prediction of Long-Term Beach Profile Evolution Due to Episodic Wave Incidence Under Tidal Environment

Abstract

Recently, studies have been conducted that long-term changes in shoreline position can be sufficiently interpreted using an ordinary differential equation that includes only erosion and recovery processes. Here, the erosion process term is given as a function of the breaking wave energy, which causes the shoreline to retreat to the ultimate erosion position by the incoming wave energy. The recovery process term is given as a function of the concentration of suspended sediment and allows it to recover to its shoreline position. Therefore, in this study, we propose a numerical technique that simulates long-term changes in the beach profile by extending the ordinary differential equation to be applied to the change in seabed constituting the beach profile by applying the parabolic equation of the equilibrium beach profile of the surf zone. This model also consists of a term that allows the beach profile to converge to the equilibrium beach profile due to the breaking wave energy and another term that allows it to converge back to the linear shoaling profile when the wave is extinguished. Therefore, it is possible to simulate the repeated formation and disappearance of scarp and berm whenever a storm wave passes, and it can also be applied to the morphological change at the beach with a large tidal range. The validity of the proposed methodology was verified by comparing the long-term shoreline observation data of Tairua Beach, New Zealand, where the tidal difference is about 2 m, with the results of the long-term beach section convergence model of this study. In addition, short-term observation data were also compared and analyzed to investigate the ability to simulate morphological changes due to episodic erosion and recovery processes. The results of this study are expected to be applied not only to the beach profile but also to the three-dimensional morphology change of the beach, and it is expected that it will serve as a cornerstone for a more detailed topographic change prediction study due to sea level rise.