Modelling of the spatial evolution of extreme laboratory wave crest and trough heights with the NLS-type equations

• The statistical properties of long-crested nonlinear wave time series measured in an offshore basin have been analyzed.
• Various models indicate that it is the modulational instability that affects the evolution process.
• Wave crest is more sensitive to the quasi-resonant four-wave interaction effect than wave trough.
• The scaled maximal wave crest presents a linear regression model with the coefficient of kurtosis.
• The observed statistical properties simulated by the NLS equations compare favourably with the experimental results.

The statistical properties of long-crested nonlinear wave time series measured in an offshore basin have been analyzed in different aspects such as the distributions of surface elevation, wave crest, wave trough, and wave period. Comparison with linear, second-order and third-order theoretical models indicates that although bound wave effects also contribute to the deviation from a Gaussian process, it is the modulational instability that primarily determines the discrepancy in the evolution process in the presence of strong nonlinearity. Interestingly enough, wave crest is more sensitive to the quasi-resonant four-wave interaction effect than wave trough and the scaled maximal wave crest presents a linear regression model with the coefficient of kurtosis. Meanwhile, the estimation of the observed statistical properties is reconstructed on the basis of an ensemble of 100 wave series simulated by the NLS-type equations and compared favourably with the experimental results in most cases. Moreover, with the increased third-order nonlinear effect the difference between NLS and Dysthe simulations is enlarged and mainly reflected on the distribution of wave crest.