Non-Gaussian Random Wave Simulation by Two-Dimensional Fourier Transform and Linear Oscillator Response to Morison Force

[+] Author and Article Information
Xiang Yuan Zheng1

Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Trondheim 7491, Norwayxiang.y.zheng@ntnu.no

Torgeir Moan

Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Trondheim 7491, Norwaytormo@ntnu.no

Ser Tong Quek

Civil Engineering Department, National University of Singapore, Singapore 117576, Singaporecveqst@nus.edu.sg


Corresponding author.

J. Offshore Mech. Arct. Eng 129(4), 327-334 (May 02, 2007) (8 pages) doi:10.1115/1.2783888 History: Received October 07, 2006; Revised May 02, 2007

The one-dimensional fast Fourier transform (FFT) has been applied extensively to simulate Gaussian random wave elevations and water particle kinematics. The actual sea elevations/kinematics exhibit non-Gaussian characteristics that can be represented mathematically by a second-order random wave theory. The elevations/kinematics formulations contain frequency sum and difference terms that usually lead to expensive time-domain dynamic analyses of offshore structural responses. 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 forward FFT are implemented, respectively, across the two dimensions of the wave interaction matrix. Given specified wave conditions, the statistics of simulated elevations/kinematics compare well with not only the empirical fits but also the analytical solutions based on a modified eigenvalue/eigenvector approach, while the computational effort of simulation is very economical. In addition, the stochastic analyses in both time domain and frequency domain show that, attributable to the second-order nonlinear wave effects, the near-surface Morison force and induced linear oscillator response are more non-Gaussian than those subjected to Gaussian random waves.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Skewness and kurtosis excess of velocity attenuate with z

Grahic Jump Location
Figure 2

Power spectrum of Morison force (at z=−3m)

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Figure 3

Power spectrum of oscillator displacement



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