Traditionally, wave parameters and their statistics has been derived from time series measurements of wave elevation. Recently, due to introduction in oceanography of stereo camera systems, increasing attention has started to be given to spatial wave data and their statistics. The present study is addressing spatial and temporal statistics of nonlinear waves, giving focus to the rogue-prone sea states observed in the North Sea. Both field data and numerical simulations are used in the analysis which includes the following wave parameters: surface elevation, wave height, wave crest, wave troughs, wave period and wave phases. Numerical simulations are carried out by the nonlinear HOSM (Higher Order Spectral Method) wave solver. The nonlinear order M in the HOSM simulations in this study is set to M=3, which includes the leading order nonlinear dynamical effects, including the effect of modulational instability. The solver includes also the linear and 2nd order wave model. The Pierson-Moskowitz and the JONSWAP spectrum with gamma parameter equal 2, 3.3 and 6, and different directional energy spreading functions are applied in the analysis. The wave steepness of the investigating sea states is varying from 0.08 to 0.16, and its impact on statistical distributions of the considered parameters is shown. Differences between temporal and spatial statistics are discussed in perspective of marine structures’ design. The results are compared with theoretical nonlinear distributions derived based on the Gram-Charlier series as well as with the commonly used in design practice linear and 2nd order statistical models. Recommendations for engineering applications are given.

Statistical Description of Nonlinear Waves

Paper Proceedings: https://asmedigitalcollection.asme.org/OMAE/OMAE2021/volume/85116

OMAE 2021

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