Monte Carlo Simulation of Random Waves at Finite Depth Based on the Joint Distribution of Wave Amplitude and its Associated Period in Nonlinear Random Waves of Finite Bandwidth

Abstract

This study aims to develop a new methodology to generate random waves from a joint distribution of wave amplitude and its associated period. In doing so, the wave spectrum was derived from the joint distribution of wave amplitude and associated period and compared with the Wallops spectrum, which has been most frequently referred to in the literature. Numerical simulation shows that the nonlinearity of random waves makes a significant difference in the wave spectrum. These differences are summarized by a somewhat excessive peak period of the semi-empirical wave spectrum and underestimating wave energy over the high-frequency band. These behavioral characteristics of wave spectrum derived from the joint distribution of wave amplitude and its associated period are conceived to be due to the intrinsic property of the nonlinear random waves. The rationale of this reasoning can be found in the fact that non-negligible amount of wave energy shifts to the relatively short and long period band due to the resonant wave-wave interaction as nonlinearity is getting more pronounced as widely known in the coastal engineering community after studies of Hasselmann(1967) and Phillips(1980) on the developments of wind waves. Among the differences mentioned above, an excessively high peak period can be fully predicted by recalling that the wave period is getting shortened due to the phase difference between the free mode waves among the higher-order harmonic components appearing in random waves due to resonant wave-wave interaction and the resulting destructive interaction.