This article concerns the calculation of the wave period probability densities in non-Gaussian mixed sea
states. The calculations are carried out by incorporating a second order nonlinear wave model into an asymptotic
analysis method which is a novel approach to the calculation of wave period probability densities. Since all of
the calculations are performed in the probability domain, the approach avoids long time-domain simulations. The
accuracy and efficiency of the asymptotic analysis method for calculating the wave period probability densities
are validated by comparing the results predicted using the method with those predicted by using the Monte-Carlo
simulation (MCS) method.
WANG Ying-guanga,b* (王迎光), XIA Yi-qinga (夏一青)
. symptotic Calculation of Wave Period Statistics in Non-Gaussian Mixed Sea[J]. Journal of Shanghai Jiaotong University(Science), 2013
, 18(1)
: 54
-60
.
DOI: 10.1007/s12204-013-1368-3
[1] Cavanie A, Arhan M, Ezraty R. A statistical relationship between individual heights and periods of storm waves [C]//Proceedings of the Conference on Behaviour of Offshore Structures. Trondheim: [s.n.],1976: 354-360.
[2] Longuet-Higgins M S. On the joint distribution of the periods and amplitudes of sea waves [J]. Journal of Geophysical Research, 1975, 80(18): 2688-2694.
[3] Longuet-Higgins M S. On the joint distribution of wave periods and amplitudes in a random wave field [C]//Proceedings of the Royal Society of London A. London: Royal Society Publishing, 1983: 241-258.
[4] Lindgren G, Rychlik I, Prevosto M. The relation between wave length and wave period distributions in random Gaussian waves [J]. International Journal of Offshore and Polar Engineering, 1998, 8(4): 258-264.
[5] Xu D L, Li X, Zhang L Z, et al. On the distributions of wave periods, wavelengths, and amplitudes in a random wave field [J]. Journal of Geophysical Research, 2004, 109: C05016.1-16.
[6] Stansell P, Wolfram J, Linfoot B. Improved joint probability distribution for ocean wave heights and periods [J]. Journal of Fluid Mechanics, 2004, 503: 273-297.
[7] Ochi M K. Ocean waves, the stochastic approach [M]. Cambridge: Cambridge University Press, 2005.
[8] Butler R W, Machado U B, Rychlik I. Distribution of wave crests in a non-Gaussian sea [J], Applied Ocean Research, 2009, 31: 57-64.
[9] Machado U B. Probability density functions for nonlinear random waves and responses [J]. Ocean Engineering, 2003, 30: 1027-1050.
[10] Zheng X Y, Moan T, Quek S T. Non-Gaussian random wave simulation by two-dimensional Fourier transform and linear oscillator response to Morison force [J]. Journal of Offshore Mechanics and Arctic Engineering, 2007, 129(4): 327-334.
[11] Brodtkorb P A. The probability of occurrence of dangerous wave situations at sea [D]. Trondheim, Norway: Faculty of Engineering Science and Technology, Norwegian University of Science and Technology, 2004.
[12] Rodr′guez G R, Soares C G, Pacheco M, et al. Wave height distribution in mixed sea-states [J]. Journal of Offshore Mechanics and Arctic Engineering, 2002, 124: 34-40.
[13] Arena F, Soares C G. Nonlinear crest, trough, and wave height distributions in sea states with doublepeaked spectra [J]. Journal of Offshore Mechanics and Arctic Engineering, 2009, 131: 041105.1-8.
[14] Rodr′guez G R, Soares C G. The bivariate distribution of wave heights and periods in mixed sea states [J]. Journal of Offshore Mechanics and Arctic Engineering, 1999, 121(2): 102-106.
[15] Rodr′guez G R, Soares C G. Correlation between successive wave heights and periods in mixed sea states [J]. Ocean Engineering, 2001, 28(8): 1009-1030.
[16] Rodr′guez G R, Soares C G, Pacheco M. Wave period distribution in mixed sea-states [J]. Journal of Offshore Mechanics and Arctic Engineering, 2004, 126: 105-112.
[17] Hasselmann K. On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory [J]. Journal of Fluid Mechanics, 1962, 12: 481-500. [18] Marthinsen T. On the statistics of irregular secondorder waves [R]. Stanford: Stanford University, 1992.
[19] Zahle U. A general Rice formula, Palm measures, and horizontal-window conditioning for random fields [J]. Stochastic Process and Applications, 1984, 17: 265-283.
[20] Wang Ying-guang. Research on slow drift extreme response and stability of ocean structures in random seas [D]. Shanghai: School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, 2008: 27-32 (in Chinese).
[21] Wang Y G, Xue L P, Tan J H. Surge response of a compliant offshore structure by time domain simulation [J]. Journal of Shanghai Jiaotong University: Science, 2007, 12(6): 838-844.
