The harmonic structure of the focused wave in a wave flume

In recent years, extreme waves have attracted more and more attention due to its threat to offshore and coastal structures. It is essential to obtain further insight into the formation and propagation of the extreme waves. The formation of extreme waves mainly comes from the simultaneous focusing of wave group energy in the ocean. In the present study, the nonlinear characteristics of the extreme wave are experimentally investigated by the wave focusing method. The phase decomposition methods, both two-phases separation and four-phases separation methods, are used to obtain the higher harmonic elevation in the focused wave. The results show that the four-phases separation method can reasonably extract the first four harmonics. With the separated results, the nonlinear analysis of the wave elevation and velocity of the focused wave is carried out. It is found that the harmonics of the wave group focused at the same time, but the wave elevation and energy of higher-order harmonics are smaller than that of the overall wave. The Stokes wave theory can describe the variation of second-order harmonics satisfactorily. However, the Stokes wave theory cannot estimate third-order harmonics accurately. More work should be carried out to figure out the third-order wave interaction occurring during wave focusing. With a distributed wave gauge system, the wave evolution along the wave flume is measured. The evanescent modes significantly influence the wave group's harmonic structure near the wavemaker. The coefficients of the higher-order harmonics are obtained from the measured elevations. The nonlinear wave elevation of the focused wave can be reconstructed with those coefficients basing on the linear theoretical solution, which is in good agreement with the experimental results.