A forecast model of freak wave generations in deep water

In ocean engineering designs, random extreme events are the most difficultly determined environmental load factors. Appearances of freak waves in the normal sea states are just such events. To reduce their potential destruction of marine structures, a forecast model is studied to predict whether freak waves occur in the wave propagation. In this model, the modified fourth-order nonlinear Schrödinger equation is employed as the deep-water wave model, which controls the evolution of complex wave envelopes. The measured wave train is set as its initial condition which needs to be changed into its corresponding complex wave envelope by use of the Hilbert transform method to be input into the wave model. During the evolution of complex wave envelope, its corresponding wave heights are estimated and compared with the definition of freak waves. If a freak wave is captured, its occurrence position and time are given. Three cases of observed, simulated and laboratory wave trains as initial conditions are performed to predict the generation of freak waves. Results show that measured wave trains can be simply and accurately input into this forecast model through the Hilbert transform method and this model can predict the generation of freak waves within some space and time in its traveling. In addition, larger groups than usual group height or length increase the probability of freak wave generation. This forecast model may provide marine activities with a safety warning in some open seas.