A probability-based superposition model of freak wave simulation

• The occurrence probability of freak waves generated is deduced in this paper.
• A method to decide the wave-component number is proposed.
• The concept of the conserved wave-absorbing method is proposed in this paper.
• Simulation efficiency is improved using the probability-based method.

The superposition model can generate freak waves in the specified location and time, thus becoming a common model for simulation of freak waves numerically and experimentally. However sometimes the superposition model does not meet the actual wave energy of random sea states and the simulation efficiency may not be high when the energy of focusing wave train is low. In this paper, the occurrence probability of freak waves generated using the superposition model is obtained based on which a method is developed to determine the number of wave components of the focusing wave train. The probability-based superposition model reduces energy proportion of the focusing wave train, and improves the simulation efficiency of freak waves based on the superposition model. Using the probability-based superposition model, a numerical wave tank (NWT) is created which solves the 2-D Navier–Stokes equations. Validity of the probability-based superposition model is proved by comparing the simulated freak waves with freak waves recorded both under the sea states of Japan and in the laboratory. When establishing the numerical wave tank, a new wave-absorbing method is developed to reduce the length of the absorbing region and to determine the absorbing weight.