Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T19:06:57.384Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient Computation of Nonlinear Crest Distributions for Irregular Stokes Waves

Part of: Probabilistic methods, simulation and stochastic differential equations Incompressible inviscid fluids

Published online by Cambridge University Press:  12 April 2016

Ying-Guang Wang
Ying-Guang Wang*
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China and State Key laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
*
*Corresponding author. Email address:wyg110@sjtu.edu.cn (Y.-G.Wang)
Get access

Abstract

This paper concerns the computation of nonlinear crest distributions for irregular Stokes waves, and a numerical algorithm based on the Fast Fourier Transform (FFT) technique has been developed for carrying out the nonlinear computations. In order to further improve the computational efficiency, a new Transformed Rayleigh procedure is first proposed as another alternative for computing the nonlinear wave crest height distributions, and the corresponding computer code has also been developed. In the proposed Transformed Rayleigh procedure, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure have been applied for calculating the wave crest distributions of a sea state with a Bretschneider spectrum and a sea statewith the surface elevation datameasured at the Poseidon platform. It is demonstrated in these two cases that the numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure can offer better predictions than those from using the empirical wave crest distribution models. Meanwhile, it is found that our proposed Transformed Rayleigh procedure can compute nonlinear crest distributions more than 25 times faster than the numerical algorithm based on the FFT technique.

Keywords

Irregular Stokes wavescrest distributionTransformed Rayleigh procedureFast Fourier Transform (FFT) technique

MSC classification

Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction 65C50: Other computational problems in probability 65C60: Computational problems in statistics 65C05: Monte Carlo methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 881 - 903
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Chakrabarti, S.K., Handbook of Offshore Engineering, Elsevier Science, (2005): 197–277.Google Scholar
[2]Al-Salem, K., Al-Nassar, W., Tayfun, A., Risk analysis for capsizing of small vessels, Ocean Eng., 33 (2006): 788–797.CrossRefGoogle Scholar
[3]Longuet-Higgins, M.S., On the statistical distribution of the heights of seawaves, J. Mar. Res., 11 (1952): 245–266.Google Scholar
[4]Chakrabarti, S.K., Hydrodynamics of Offshore Structures. Computational Mechanics Publications Inc., 1987.Google Scholar
[5]Ochi, M.K., OceanWaves, The Stochastic Approach, Cambridge University Press, (1998): 2–4.CrossRefGoogle Scholar
[6]Onorato, M., Osborne, A.R., Serio, M., Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments, Phys. Rev. E, 70 (2004): 067302, 1–4.Google Scholar
[7]Fedele, F., On wave groups in a Gaussian sea, Ocean Eng., 33 (2006): 2225–2239.Google Scholar
[8]Janssen, P.A.E.M., Nonlinear four-wave interactions and freak waves, J. Phys. Oceanogr., 33 (2003): 863–884.2.0.CO;2>CrossRefGoogle Scholar
[9]Dyachenko, A.I., and Zakharov, V.E., Modulation instability of stokes wave freak wave, JETP Letters, 81(6) (2005): 255–259.CrossRefGoogle Scholar
[10]Zakharov, V.E. and Shamin, R.V., Probability of the occurrence of freak waves, JETP Letters, 91(2) (2010): 62–65.CrossRefGoogle Scholar
[11]Forristall, G.Z., Wave crest distributions: Observations and second-order theory, J. Phys. Oceanogr., 30:8 (2000): 1931–1943.Google Scholar
[12]Tayfun, M.A., Narrow-band nonlinear sea waves, J. Geophys. Res., 85 (1980): 1548–1552.Google Scholar
[13]Lukomsky, V.P., Gandzha, I.S., Lukomsky, D.V., Computational analysis of the almost-highest waves on deep water, Comput. Phys. Commun., 147(1-2) (2002): 548–551.CrossRefGoogle Scholar
[14]Lukomsky, V.P., Gandzha, I.S., Lukomsky, D.V., Steep sharp-crested gravity waves on deep water, Phys. Rev. Lett., 89(16) (2002): 164502.Google Scholar
[15]Lukomsky, V.P., Gandzha, I.S., Fractional Fourier approximations for potential gravity waves on deep water, Nonlinear Processes in Geophysics, 109(6) (2003): 599–614.Google Scholar
[16]Wang, Y.G, and Xia, Y.Q., Simulating mixed sea state waves for marine design. Appl. Ocean Res., 37 (2012): 33–44.Google Scholar
[17]Viotti, C., Dutykh, D., Dudley, J., Dias, F., The emergence of coherent wave groups in deepwater random sea, Phys. Rev. E, 87(6), 063001 (2013):1–10.Google Scholar
[18]Toffoli, A., Bitner-Gregersen, E., Onorato, M., Babanin, A.V., Wave crest and trough distributions in a broad-banded directional wave field, Ocean Eng., 35 (2008): 1784–1792.CrossRefGoogle Scholar
[19]Cooley, J.W., Tukey, J.W., An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19:90 (1965): 297–301.Google Scholar
[20]Yan, H.M., Liu, Y.M., An efficient high-order boundary element method for nonlinear wave-wave and wave-body interactions, J. Comput. Phys., 230 (2011): 402–424.Google Scholar
[21]http://www.mathworks.cn/cn/help/matlab/ref/fft.html.Google Scholar
[22]Sharma, J.N., Dean, R.G., Second order directional seas and associated wave forces, Soc. Petroleum Engineers J., 4, (1981): 129–140.CrossRefGoogle Scholar
[23]Smith, S.F., Hoyle, M.J.R., Ahilan, R.V., Hunt, R.J., Marcom, M.R., 3D nonlinear wave spreading on jackup loading and response and its impact on current assessment practice, Offshore Technology Conference, (2006): OTC 18266, 1-13.Google Scholar
[24]Marthinsen, T., On the Statistics of Irregular Second-OrderWaves, Stanford Report RMS-11, 1992.Google Scholar
[25]Langley, R.S., A statistical analysis of non-linear random waves, Ocean Eng., 14(5) (1987): 389–407.Google Scholar
[26]Hasselmann, K., On the non-linear energy transfer in a gravity-wave spectrum Part I. General theory. J. Fluid Mech., 12 (1962): 481–500.Google Scholar
[27]Krasitskii, V.P., Canonical transformation in a theory of weakly nonlinear waves with a non-decay dispersion law, Sov. Phys. JETP, 71(5) (1990): 921–927.Google Scholar
[28]Shinozuka, M., Deodatis, G., Simulation of stochastic processes by spectral representation, Appl. Mech. Rev. ASME, 44:4 (1991): 191–204.Google Scholar
[29]Ochi, M.K., Probability distribution applicable to non-Gaussian random processes, Probabilist. Eng. Mech., 9 (1994): 255–264.Google Scholar
[30]Wang, Y.G., and Xia, Y.Q., Calculating nonlinear wave crest exceedance probabilities using a Transformed Rayleigh method, Coast. Eng., 78 (2013): 1–12.Google Scholar
[31]Kiyokazu, Y., Yutaka, O., Masakatsu, S., Kinji, S., At sea experiment of a floating offshore structure, Part 5, Measurement of stress range distributions for fatigue analysis, J. Soc.Naval Architects Japan, 170, (1991): 609-618. (In Japanese).Google Scholar
[32]http://code.google.com/p/wafo/downloads/detail?name=wafo25.7z.Google Scholar