A numerical study of the breaking of modulated waves generated at a wave maker

This paper is concerned with breaking criteria for generated waves. An input in the form of a time signal is prescribed to a wave maker located at one end of a wave tank as used in hydrodynamic laboratories. The motion of this wave maker produces waves propagating into initially still water in the tank. The spatial evolution of the wave train is referred to as the signaling problem to distinguish from an initial value problem that investigates the temporal evolution of a given initial wave profile. A numerical simulation of the nonlinear propagation of time traces along the tank is investigated to see if breaking occurs and, if so, at which location in the tank. A quantity is proposed as a breaking indicator that is based on a modification of a mean convergence rate of the squared steepness, recently suggested by Song and Banner for the initial value problem. Two classes of waves, namely Benjamin-Feir and bichromatic waves, are considered as influx to the wave maker. A comparison between the signaling problem and the initial value problem for these two classes is presented. The result of the investigations is that, for both classes, the initial steepness can be more extreme in the signaling case than in the case of the initial value problem such that there is no breaking during their evolution. Furthermore, the modified quantity shows the existence of a threshold value for breaking, below which no breaking can occur.