Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29209

Select areas to restrict search in scientific publication database:
Spurious Crests in Second-Order Waves
Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.
Digital Object Identifier (DOI):


[1] R. G. Dean, and R. A. Dalrymple, Water Wave Mechanics for Engineers and Scientist., New Jersey: World Scientific, 1991, pp. 295-305.
[2] R. Miche, "Mouvements ondulatoires de la mer en profoundeur onstante ou decroissante. Annales des Ponts et Chaussees," vol. 121, pp. 285-318, 1944.
[3] M. P. Tulin, and J. J. Li, "On the breaking of energetic waves," Inter. J. Offshore Polar Eng.,vol. 2, pp. 46-53, 1992.
[4] M. A. Tayfun, "Distributions of envelope and phase in wind waves," J. Phys. Oceanogr., vol. 38, pp. 2784-2800, 2008.
[5] Z. Cherneva, M. A. Tayfun , and C. Guedes Soares, 2009. "Statistics of nonlinear waves generated in an offshore wave basin," J. Geophys. Res., vol. 114, C08005, doi:10.1029/2009JC005332, 2009.
[6] A. Toffoli, A. Babanin, M. Onorato, and T. Waseda, " Maximum steepness of oceanic waves: field and laboratory experiments," Geophys. Res. Lett., vol. 37, L05603, doi:10.1029/2009GL041771, 2010.
[7] J. N. Sharma, and R. G. Dean, "Development and evaluation of a procedure for simulating a random directional second order sea surface and associated wave forces," Ocean Eng. Rep.20, University of Delaware, Newark. 1979.
[8] M. S. Longuet-Higgins, "The effects of nonlinearities on statistical distributions in the theory of sea waves," J. Fluid Mech. vol. 17, pp. 459-480, 1963.
[9] L. Weber, and D. E. Barrick, "On the nonlinear theory for gravity waves on the ocean-s surface. Part I: derivations," J. Phys. Oceanogr., vol. 7, pp. 3-10, 1977.
[10] G. Z. Forristall, "Wave crest distributions: observations and secondorder theory," J. Phys. Oceanogr., vol. 30, pp. 1931-1943, 2000.
[11] M. A. Tayfun, "Distributions of envelope and phase in weakly nonlinear Random waves," J. Eng. Mech., vol. 120, pp. 1009-1025, 1994.
[12] M. A. Tayfun, "Narrow-band nonlinear sea waves," J. Geophys. Res., vol. 85, pp. 1548-1552, 1980.
[13] M. A. Tayfun, and J-M. Lo, "Envelope, phase, and narrowband models of sea waves," J. Waterw. Port, Coast. Ocean Eng., vol. 115, pp. 594- 613, 1990.
[14] F. Arena, and F. Fedele, "A family of narrow-band nonlinear stochastic processes for the mechanics of sea waves," Eur. J. Mech. B/Fluids, vol. 21, pp. 125-137, 2005.
[15] M. A. Tayfun,"Distribution of large wave heights," J. Waterway, Port, Coast. Ocean Eng., vol. 116, pp. 686-707, 1990.
[16] P. Boccotti, "On mechanics of irregular gravity waves," Atti Acc. Naz. Lincei Memorie, vol. 19, pp. 111-170, 1989.
[17] P. Boccotti, Wave mechanics for ocean engineering, Oxford: Elsevier Science, 2000, pp. 475-485.
[18] F. Arena, "On non-linear very large sea wave groups," Ocean Eng., vol. 32, pp. 1311-1331, 2005.
[19] F. Fedele, and F. Arena, "Weakly nonlinear statistics of high random waves," Phys. Fluids, vol. 17, pp. 026601:1-10, 2005.
[20] F. Fedele, and M. A. Tayfun," On nonlinear wave groups and crest statistics," J. Fluid Mech., vol. 620, pp. 221-239, 2009.
[21] M. A. Tayfun, and F. Fedele, "Wave-height distributions and nonlinear effects," Ocean Eng., vol. 34, pp. 1631-1649, 2007.
[22] M. A. Tayfun,"On the distribution of wave heights: nonlinear effects," in Marine Technology and Engineering, vol. 1, C. Guedes Soares, Y. Garbatov, N. Fonseca, and A. P. Teixeira, Eds. London: Taylor & Francis Group, 2011, pp. 247-268.
[23] G. Lindgren, "Local maxima of Gaussian fields," Arkiv f¨ür Matematik, vol. 10, pp. 195-218, 1972.
[24] O. M. Phillips, D. Gu, and M. Donelan, "On the expected structure of extreme waves in a Gaussian sea. I. Theory and SWADE buoy measurements," J. Phys. Oceanogr., vol. 23, pp. 992-1000, 1993.
[25] A. Toffoli, E. Bitner-Gregersen, M. Onorato, A. R. Osborne, and A. V. Babanin, "Surface gravity waves from direct numerical simulations of the Euler equations: A comparison with second-order theory," Ocean Eng., vol. 35, pp. 367-379, 2008.
[26] M. A. Tayfun, "Statistics of nonlinear wave crests and groups," Ocean Eng., vol. 33, pp.1589-1622, 2006.
[27] M. A. Tayfun, "A modified probability distribution for describing second-order sea waves," unpublished.
[28] M. S. Longuet-Higgins, The statistical analysis of a random moving surface. Philos. Trans. Roy. Soc. London, A966, pp. 321-387, 1957.
[29] M. A. Tayfun, and F. Fedele, "Expected shape of extreme waves in storm seas," in Proc. 26th Inter. Conf. on Offshore Mech.& Arctic Eng., San Diego, paper no. OMAE2007-29073, pp. 1-8, 2007.
[30] M. A. Donelan, J. Hamilton, and W. H. Hue, "Directional spectra of wind-generated waves," Philos. Trans. Roy. Soc. London, A315, pp. 509-562, 1985.
Vol:13 No:01 2019
Vol:12 No:12 2018Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007