Wj. Pierson et A. Jean-pierre, Monte Carlo simulations of nonlinear ocean wave records with implications for models of breaking waves, J SHIP RES, 43(2), 1999, pp. 121-134
A Monte Carlo method for simulating nonlinear ocean wave records as a funct
ion of time is described. It is based on a family of probability density fu
nctions 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 re
cord. 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 t
he nonlinear equations that describe unbroken waves. It yields a simulated
wave record that reproduces the chosen values for the skewness and, if need
ed, the kurtosis of a wave record so that the statistical properties are mo
deled. 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 o
f the nonlinear properties of wave records. The need for a nonlinear model
of waves for naval architecture, remote sensing and other design problems i
s shown. This method cannot provide any information on whether a particular
wave will break. Some of the recent results on breaking waves and "green w
ater" are reviewed. The possibility that this method can be extended based
on the concept of a "local absorbing patch" is described.