Nonlinear crest distribution for shallow water Stokes waves

This article concerns the calculation of nonlinear crest distribution for shallow water Stokes waves. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic analysis method. This is a new approach to the calculation of wave crest distribution, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The accuracy and efficiency of this new approach for calculating the wave crest distribution are validated by comparing the results predicted using it with those predicted by using the Monte Carlo simulation (MCS) method, by using a previous Transformed Rayleigh method, by using some existing wave crest distribution formulas, and by using the measured surface elevation data at the Poseidon platform in the Japan Sea.