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.

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

Xiang Yuan Zheng

,
Xiang Yuan Zheng

Centre for Ships and Ocean Structures,

xiang.y.zheng@ntnu.no
Norwegian University of Science and Technology

, Trondheim 7491, Norway
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Torgeir Moan

,
Torgeir Moan

Centre for Ships and Ocean Structures,

tormo@ntnu.no
Norwegian University of Science and Technology

, Trondheim 7491, Norway
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Ser Tong Quek

Ser Tong Quek

Civil Engineering Department,

cveqst@nus.edu.sg
National University of Singapore

, Singapore 117576, Singapore
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Xiang Yuan Zheng

Centre for Ships and Ocean Structures,

Norwegian University of Science and Technology

, Trondheim 7491, Norwayxiang.y.zheng@ntnu.no

Torgeir Moan

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

*J. Offshore Mech. Arct. Eng*. Nov 2007, 129(4): 327-334 (8 pages)

**Published Online:**May 2, 2007

Article history

Received:

October 7, 2006

Revised:

May 2, 2007

Citation

Zheng, X. Y., Moan, T., and Quek, S. T. (May 2, 2007). "Non-Gaussian Random Wave Simulation by Two-Dimensional Fourier Transform and Linear Oscillator Response to Morison Force." ASME. *J. Offshore Mech. Arct. Eng*. November 2007; 129(4): 327–334. https://doi.org/10.1115/1.2783888

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