Wave run-up on a vertical wall protected by a submerged breakwater

Submerged breakwaters have been constructed in coastal zones for shorelineor harbour protection or to prevent beach erosion. In the paper, the waverun-up on a vertical wall protected by a submerged breakwater is analyzed.The physical configurations include a rigid barrier and a semi-infinitelylong channel with finite depth. By means of numerical wave flume technique,the linear incident wave propagation and run-up on the vertical wall aresimulated. In the cases of different distances between the barrier and thewall with a fixed barrier height, the results of numerical simulations showthat the wave run-up depends on the ratio of the distance to the wavelength. There is no difference of the wave run-up on the vertical wall withor without the barrier, when the barrier is located at the anti-nodes of thestanding wave; while the wave run-up with the barrier is lower than thatwithout the barrier, when the barrier is located at the nodes of thestanding wave. Based on the linear wave theory, by matching the velocityalong the barrier and along the gap, the systems of linear equations aboutthe velocity potentials are obtained, i.e. the theoretical model.Furthermore, the wave run-up is further analyzed for more various settingsof barrier height and distance between the barrier and the wall with thetheoretical model. Not only the numerical wave flume simulations, but alsothe analytical results reveal that the wave run-up on the wall stronglydepends on the distance between the barrier and the vertical wall.