Abstract
The spectral properties of Stokes waves are shown in this paper by theoretical and numerical methods. This is done by expressing wave profiles and velocities of water particles as nonlinear combinations of the first order component of wave profiles. Under the assumption of the first order wave profiles being zero mean Gaussian processes, the relationship between autocorrelation functions of wave profiles and velocities of water particles and the first order component of wave profiles is established using the nonlinear spectral analysis. The spectral densities of nonlinear random waves, the velocities and accelerations of water particles are then obtained. Numerical computations are carried out to analyze the effect of fundamental parameters of waves. The results indicate that wave height is the most sensible parameter to the root mean squares related and wave depth is the least sensible one of all.
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