On narrow‐band representation of ocean waves: 2. Simulations

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Abstract
In paper 1 (Tayfun, this issue) we derived two narrow‐band type representations for nonlinear waves and obtained theoretical expressions for the key statistics of the corresponding surface elevations, namely, the variance, skewness, and kurtosis. The nature of these statistics and the underlying probability structure were examined qualitatively with particular emphasis on the effects of the spectrum bandwidth. In this paper we explore the reliability of these results quantitatively. Proceeding via the Monte Carlo approach and finite Fourier transform techniques, we generate extensive samples of surface time history with preassigned spectral and statistical properties. Each sample is synthesized from a systematic superposition of the first‐order linear field and the second‐order corrections, consisting of shortwave and long‐wave modulations, respectively. This approach enables us to demonstrate explicitly the individual as well as combined effects of second‐order nonlinearities on the probability distribution and statistics of the surface elevation. In the final analysis we find that the simulated results compare favorably with the theoretical predictions and confirm the validity of various qualitative arguments put forward in paper 1.

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