Simulations of Extreme Wave Runup on a Vertical Wall by Analytic Boussinesq Model

Wave runup on a vertical wall has both fundamental and practical interest. The wave impact on a structure is an important aspect that must be taken into account in the design of coastal structures. From linear wave theory, it is known that the wave amplitude on a vertical fully reflecting wall is twice the amplitude of the incoming wave. The result may be different for nonlinear dispersive waves. Following [1], we show that the propagation of a short wave group of very long nonlinear monochromatic waves above a flat bottom, can increase the amplitude nonlinearly in the travel to a wall, and produce much higher amplitudes on the wall compared to the initial amplitude: the amplification of such a wave can reach six times the initial amplitude. The strong amplification due to the combined action of nonlinear steepening and dispersion before the wall leads to waves that resemble undular bores. Using the same principles, we show that the propagation of a focusing wave group to a wall that is located at the focusing point of the wave can produce an extreme runup with 11 times amplification of the maximum initial amplitude. The simulations are done by HAWASSI-AB, a spatial-spectral implementation of Analytic Boussinesq model [2].