Monte Carlo simulations of nonlinear ocean wave records with implications for models of breaking waves

A Monte Carlo method for simulating nonlinear ocean wave records as a function of time is described. It is based on a family of probability density functions developed by Karl Pearson and requires additional knowledge of the dimensionless moments of a postulated nonlinear wave record, which are the skewness and kurtosis. A frequency spectrum is used to simulate a linear record. It is then transformed to a nonlinear record for the chosen values of the skewness and kurtosis. The result is not a perturbation expansion of the nonlinear equations that describe unbroken waves. It yields a simulated wave record that reproduces the chosen values for the skewness and, if needed, the kurtosis of a wave record so that the statistical properties are modeled. A brief history of the development of the linear model, presently in use, is given along with a survey of wave data that show the variability of the nonlinear properties of wave records. The need for a nonlinear model of waves for naval architecture, remote sensing and other design problems is shown. This method cannot provide any information on whether a particular wave will break. Some of the recent results on breaking waves and "green water" are reviewed. The possibility that this method can be extended based on the concept of a "local absorbing patch" is described.