{"title":"A Simplified Distribution for Nonlinear Seas","authors":"M. A. Tayfun, M. A. Alkhalidi","volume":97,"journal":"International Journal of Environmental and Ecological Engineering","pagesStart":34,"pagesEnd":38,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10000260","abstract":"
The exact theoretical expression describing the
\r\nprobability distribution of nonlinear sea-surface elevations derived
\r\nfrom the second-order narrowband model has a cumbersome form
\r\nthat requires numerical computations, not well-disposed to theoretical
\r\nor practical applications. Here, the same narrowband model is reexamined
\r\nto develop a simpler closed-form approximation suitable
\r\nfor theoretical and practical applications. The salient features of the
\r\napproximate form are explored, and its relative validity is verified
\r\nwith comparisons to other readily available approximations, and
\r\noceanic data.<\/p>\r\n","references":"[1] M. A. Tayfun, \u201cNarrow-band nonlinear sea waves,\u201d J. Geophys. Res.,\r\nvol. 85, pp. 1548\u20131552, 1980.\r\n[2] H. Socquet-Juglard, K. Dysthe, K. Trulsen, H. Krogstad, and J. Liu,\r\n\u201cProbability distributions of surface gravity waves during spectral\r\nchanges,\u201d J. Fluid Mech., vol. 542, 195\u2013216, 2005.\r\n[3] M. S. Longuet-Higgins, \u201cThe effects of nonlinearities on statistical\r\ndistributions in the theory of sea waves,\u201d J. Fluid Mech. vol. 17, pp.\r\n459\u2013480, 1963.\r\n[4] M. A. Tayfun, and J-M. Lo, \u201cEnvelope, phase, and narrowband models\r\nof sea waves,\u201d J. Waterw. Port, Coast. Ocean Eng., vol. 115, pp. 594-\r\n613, 1990.\r\n[5] M. A. Tayfun, \u201cStatistics of nonlinear wave crests and groups,\u201d Ocean\r\nEng., vol. 33, 1589\u20131622, 2006.\r\n[6] M. A. Tayfun, and F. Fedele, \u201cWave-height distributions and nonlinear\r\neffects,\u201d Ocean Eng., vol. 34, 1631 \u2013 1649, 2007.\r\n[7] M. A. Tayfun, and F. Fedele, \u201cExpected shape of extreme waves in\r\nstorm seas,\u201d in Proc. 26th Inter. Conf. on Offshore Mech.& Arctic Eng.,\r\nSan Diego, paper no. OMAE2007-29073, pp. 1-8, 2007.\r\n[8] M. A. Tayfun, \u201cDistributions of envelope and phase in wind waves,\u201d J.\r\nPhys. Oceanogr., vol. 38, pp. 2784\u20132800, 2008.\r\n[9] A. Toffoli, E. Bitner-Gregersen, M. Onorato, A. R. Osborne, and A. V.\r\nBabanin, \u201cSurface gravity waves from direct numerical simulations of\r\nthe Euler equations: A comparison with second-order theory,\u201d Ocean\r\nEng., vol. 35, 367\u2013 379, 2008.\r\n[10] Z. Cherneva, M. A. Tayfun, and C. Guedes-Soares, \u201cStatistics of\r\nnonlinear waves generated in an offshore wave basin\u201d, J. Geophys. Res.,\r\nvol. 114, C08005, 2009.\r\n[11] F. Fedele, and M. A. Tayfun, \u201cOn nonlinear wave groups and crest\r\nstatistics,\u201d J. Fluid Mech., vol. 620, 221\u2013239, 2009.\r\n[12] F. Fedele, Z. Cherneva, M. A. Tayfun, and C. Guedes-Soares,\r\n\u201cNonlinear Schr\u00f6dinger invariants and wave statistics,\u201d Phys. Fluids,\r\nvol. 22, 2010.\r\n[13] F. Arena, and F. Fedele, \u201cA family of narrow-band nonlinear stochastic\r\nprocesses for the mechanics of sea waves,\u201d Eur. J. Mech. B\/Fluids, vol.\r\n21, pp. 125\u2013137, 2005.\r\n[14] A. K. Jha, and S. R. Winterstein,\u201dNon-linear random ocean waves:\r\nprediction and comparison with data,\u201d in Proc. ETCE\/OMAE2000 Joint\r\nConference Energy for the New Millenium, vol. 1, paper OMAE2000-\r\n6125, 2000, ISBN: 0791819949, 9780791819944.\r\n[15] M. Prevosto, H. E. Krogstad, and A. Robin, \u201cProbability distributions\r\nfor maximum wave and crest heights,\u201d Coastal Eng., vol. 40, 329\u2013360,\r\n2000.\r\n[16] M. Abramowitz, and I. A. Stegun, Handbook of Mathematical\r\nFunctions, Dover Publications, New York, 1968, p. 932.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 97, 2015"}