Maximum Run-Up and Alongshore Mass Transport Due to Edge Waves

Abstract

The edge wave on a uniform-sloped seabed was described by the velocity-potential function by Mok and Yeh in 1999. Edge waves cannot be extended above a certain level from the still-water level, and the upper limit of the run-up of the edge waves for given conditions is found here. In this study, quantitative mass transport by the edge waves of the beach is introduced. The maximum run-up height is decided from the wave’s amplitude at shoreline, and the maximum run-up distance from the shoreline is proportional to the wavelength of the edge waves. The fluid alongshore-mass-transport profile shows that the strongest mass transport rate corresponds to the position offshoreward multiplied by 0.0362 times the wavelength, and its magnitude is 1.23 times the mass-transport rate at the shoreline. The maximum cross-sectional total mass-transport rate is 0.214 times the mass transport at the shoreline, multiplied by the wavelength for the maximum run-up condition. This study suggests that edge waves cannot be increased infinitely and that there is a maximum run-up on the coast.