Numerical Simulation of Non-Gaussian Wave Elevation and Kinematics Based on Two-Dimensional Fourier Transform

Abstract

The one-dimensional Fast Fourier Transform (FFT) has been extensively applied to efficiently simulate Gaussian wave elevation and water particle kinematics. The actual sea elevation/kinematics exhibit non-Gaussianities that mathematically can be represented by the second-order random wave theory. The elevation/kinematics formulation contains double-summation frequency sum and difference terms which in computation make the dynamic analysis of offshore structural response prohibitive. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency difference terms, inverse FFT and FFT are respectively implemented across the two dimensions of the wave interaction matrix. Given specified wave conditions, not only the wave elevation but kinematics and associated Morison force are simulated. Favorable agreements are achieved when the statistics of elevation/kinematics are compared with not only the empirical fits but the analytical solutions developed based on modified eigenvalue/eigenvector approach, while the computation effort is very limited. In addition, the stochastic analyses in both time-and frequency domains show that the near-surface Morison force and induced linear oscillator response exhibits stronger non-Gaussianities by involving the second-order wave effects.