Abstract
This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.
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References
Arhan, M. and Plaisted, R.O., 1981. Non-linear deformation of seawave profiles in intermediate and shallow water, Oceanologica Acta, 4(2), 107–115.
Baxevani, A., Hagberg, O. and Rychlik, I., 2005. Note on the distribution of extreme wave crests, Proceedings of 24th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2005), Halkidiki, Greece, Paper No. OMAE2005-67571.
Baxevani, A., Hagberg, O. and Rychlik, I., 2009. Note on the Distribution of Extreme Wave Crests, Preprint 2009:41, Department of Mathematical Sciences, Division of Mathematical Statistics, Chalmers University of Technology, University of Gothenburg, Göteborg, Sweden.
Belyaev, Y.K., 1968. On the number of exits across the boundary of a region by a vector stochastic process, Theory of Probability & Its Applications, 13(2), 320–324.
Breitung, K., 1988. Asymptotic crossing rates for stationary Gaussian vector processes, Stochastic Processes and Their Applications, 29(2), 195–207.
Chakrabarti, S., 2005. Handbook of Offshore Engineering, Elsevier Science, Amsterdam.
Forristall, G.Z., 2000. Wave crest distributions: Observations and second-order theory, Journal of Physical Oceanography, 30(8), 1931–1943.
Hagberg, O., 2004. The Rate of Crossings of A Quadratic Form of An n-Dimensional Stationary Gaussian Process, Technical Report 2004:17, Centre for Matematical Sciences, Mathematical Statistics, Lund University.
Langley, R.S., 1987. A statistical analysis of non-linear random waves, Ocean Engineering, 14(5), 389–407.
Latheef, M. and Swan, C., 2013. A laboratory study of wave crest statistics and the role of directional spreading, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2152), 20120696.
Longuet-Higgins, M.S., 1952. On the statistical distribution of the heights of sea waves, Journal of Marine Research, 11(3), 245–266.
Machado, U. and Rychlik, I., 2003. Wave statistics in non-linear random sea, Extremes, 6(2), 125–146.
Petrova, P.G. and Soares, C.G., 2014. Distributions of nonlinear wave amplitudes and heights from laboratory generated following and crossing bimodal seas, Natural Hazards and Earth System Science, 14(5), 1207–1222.
Romolo, A. and Arena, F., 2015. On Adler space-time extremes during ocean storms, Journal of Geophysical Research, 120(4), 3022–3042.
Toffoli, A., Bitner-Gregersen, E., Onorato, M. and Babanin, A.V., 2008a. Wave crest and trough distributions in a broad-banded directional wave field, Ocean Engineering, 35(17–18), 1784–1792.
Toffoli, A., Onorato, M., Bitner-Gregersen, E., Osborne, A.R. and Babanin, A.V., 2008b. Surface gravity waves from direct numerical simulations of the Euler equations: a comparison with second-order theory, Ocean Engineering, 35(3–4), 367–379.
Wang, Y.G., 2016. Modified Rayleigh distribution of wave heights in transitional water depths, China Ocean Engineering, 30(3), 447–458.
Wang, Y.G. and Xia, Y.Q., 2012. Simulating mixed sea state waves for marine design, Applied Ocean Research, 37, 33–44.
Wang, Y.G. and Xia, Y.Q., 2013. Calculating nonlinear wave crest exceedance probabilities using a transformed Rayleigh method, Coastal Engineering, 78, 1–12.
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Foundation item: This research work was financially supported by the funding of an independent research project from the Chinese State Key Laboratory of Ocean Engineering (Grant No. GKZD010038).
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Wang, Yg. Asymptotic Calculation of the Wave Trough Exceedance Probabilities in A Nonlinear Sea. China Ocean Eng 32, 189–195 (2018). https://doi.org/10.1007/s13344-018-0020-2
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DOI: https://doi.org/10.1007/s13344-018-0020-2