Calculating nonlinear wave crest exceedance probabilities using a Transformed Rayleigh method

• A Transformed Rayleigh method has been proposed to calculate the wave crest distributions.
• The nonlinear mixed sea states have been first studied.
• Finite water depth effects are also considered in the study.

This paper concerns the calculation of the wave crest height exceedance probabilities in fully nonlinear mixed sea states. The exceedance probabilities have been calculated by incorporating a fully nonlinear wave model into a Transformed Rayleigh method. This is an efficient approach to the calculation of wave crest exceedance probabilities and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The nonlinear mixed sea states studied include a swell dominated sea state, two wind sea dominated sea states, and two states of mixed wind sea and swell with comparable energy. The wave steepness influence and the finite water depth effects are also considered in the study. The accuracy and efficiency of the Transformed Rayleigh method are validated by comparing the results predicted using the method with those predicted by using the Monte Carlo simulation method, the theoretical Rayleigh method and some empirical formulas.