Digital Simulation of Nonlinear Random Waves

Digital realizations of unidirectional nonlinear random seas correct to second order in an ocean of finite depth are simulated from three types of two-parameter theoretical spectra and are compared with measured hurricane-generated realizations by means of chi-square goodness-of-fit measures computed from the Gram-Charlier probability distribution in which the statistical measures of skewness and the excess of kurtosis are determined from the measured hurricane-generated realizations. The finite Fourier transform (FFT) algorithm is shown to be an efficient method for nonlinear simulations since the FFT coefficients are complex and, therefore, capable of retaining the nonlinear random phase interactions. The second-order nonlinear simulations demonstrate improved third-order and fourth-order statistical moments compared to the linear Gaussian simulations. Previous comparisons with measured wave forces on cylindrical pilings have demonstrated improvements in the statistics of random wave force predictions computed by digital filter methods as a result of these improved nonlinear random sea simulations.