Numerical Simulation of Wave Breaking

Abstract

AbstractThe wave breaking events in a continuous spectrum of surface gravity waves are investigated numerically in 2D within a framework of the potential motion model. It is claimed that the major physical mechanism leading to wave breaking is “squeezing” of relatively short waves by the surface currents due to longer waves (the “concertina” effect), which causes the shorter waves to steepen and become unstable. It is demonstrated that locations of the breaking events are well correlated with the maximum of local current convergence, although slightly worse correlation of the locations with the local steepness of undulating surface cannot reliably exclude the latter mechanism either. It is found also that the breaking events are very rare for random surfaces with a root-mean-square (RMS) current gradient below a threshold value of about 1 s−1.The process of wave breaking was investigated by two numerical codes. One of them is based on approximation of continuous media with a discrete Hamiltonian system, which can be integrated in time very efficiently and accurately but is limited to single-valued profiles. The other is the Laplacian approach, which can explicitly exhibit the overturning of plunging breakers. Study of the discrete system shows that wave breaking is associated with the explosive growth of a certain spatially localized mode of the system.