0
Article

Nonlinear Space–Time Evolution of Wave Groups With a High Crest

[+] Author and Article Information
Felice Arena

Department of Mechanics and Materials, University ‘Mediterranea’ of Reggio Calabria, Loc. Feo di Vito, 89100 Reggio Calabria, Italye-mail: arena@unirc.it

Francesco Fedele

Department of Civil & Environmental Engineering, University of Vermont, Votey Building 213, Burlington, VT 05405e-mail: ffedele@emba.uvm.edu

J. Offshore Mech. Arct. Eng 127(1), 46-51 (Mar 23, 2005) (6 pages) doi:10.1115/1.1854705 History: Received November 06, 2003; Revised October 06, 2004; Online March 23, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.

References

Boccotti,  P., 1981, “On the highest waves in a stationary Gaussian process,” Atti Accad. Ligure Sci. Lett., Genoa, 38, pp. 271–302.
Boccotti,  P., 1982, “On ocean waves with high crests,” Meccanica, 17, pp. 16–19.
Boccotti,  P., 1983, “Some new results on statistical properties of wind waves,” Appl. Ocean. Res., 5, pp. 134–140.
Boccotti,  P., 1989, “On mechanics of irregular gravity waves,” Atti Accad. Naz. Lincei, Mem., Cl. Sci. Fis., Mat. Nat., Sez. 1a, 19, pp. 11–170.
Boccotti,  P., 1997, “A general theory of three-dimensional wave groups,” Ocean Eng., 24, pp. 265–300.
Boccotti, P., 2000, Wave mechanics for ocean engineering, Elsevier Science, Oxford.
Boccotti,  P., 1995, “A field experiment on the small-scale model of a gravity offshore platform,” Ocean Eng., 22, pp. 615–627.
Boccotti,  P., 1996, “Inertial wave loads on horizontal cylinders: a field experiment,” Ocean Eng., 23, pp. 629–648.
Boccotti,  P., Barbaro,  G., and Mannino,  L., 1993, “A field experiment on the mechanics of irregular gravity waves,” J. Fluid Mech., 252, pp. 173–186.
Boccotti,  P., Barbaro,  G., and Fiamma,  V. , 1993, “An experiment at sea on the reflection of the wind waves,” Ocean Eng., 20, pp. 493–507.
Phillips,  O. M., Gu,  D., and Donelan,  M., 1993, “On the expected structure of extreme waves in a Gaussian sea, I. Theory and SWADE buoy measurements,” J. Phys. Oceanogr., 23, pp. 992–1000.
Phillips,  O. M., Gu,  D., and Walsh,  E. J., 1993, “On the expected structure of extreme waves in a Gaussian sea, II. SWADE scanning radar altimeter measurements,” J. Phys. Oceanogr., 23, pp. 2297–2309.
Lindgren,  G., 1970, “Some properties of a normal process near a local maximum,” Ann. Math. Stat., 41(6), pp. 1870–1883.
Lindgren,  G., 1972, “Local maxima of Gaussian fields,” Ark. Matematik, 10, pp. 195–218.
Tromans, P. S., Anaturk, A. R., and Hagemeijer, P., 1991, A new model for the kinematics of large ocean waves-application as a design wave-Shell International Research, publ. 1042.
Sharma, J. N., and Dean, R. G., 1979, Development and Evaluation of a Procedure for Simulating a Random Directional Second Order Sea Surface and Associated Wave Forces, Ocean Engineering Report No. 20, University of Delaware.
Tayfun,  M. A., 1986, “On Narrow-Band Representation of Ocean Waves,” J. Geophys. Res., [Atmos.], 91(6), pp. 7743–7752.
Fedele, F., Arena, F., 2003, “On the statistics of high non-linear random waves,” Proc. 13th Int. Offshore and Polar Engng Conf. (ISOPE 2003), Honolulu, USA, III, 17–22.
Hasselmann, K., Barnett, T. P., Bouws, E. et al., 1973, Measurements of wind wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deut. Hydrogr. Zeit., A8, 1–95.
Jensen,  J. J., 1996, “Second-order wave kinematics conditional on a given crest,” Appl. Ocean Res. 18, pp. 119–128.
Tung,  C. C., and Huang,  N. E., 1985, “Peak and trough distributions of nonlinear waves,” Ocean Eng., 12, pp. 201–209.
Kriebel,  D. L., and Dawson,  T. H., 1991, “Nonlinear effects on wave groups in random seas,” J. Offshore Mech. Arct. Eng., 113, pp. 142–147.
Forristall,  G. Z., 2000, “Wave crest distributions: observations and second-order theory,” J. Phys. Oceanogr., 30(8), pp. 1931–1943.
Prevosto,  M., Krogstad,  H. E., and Robin,  A., 2000, “Probability distributions for maximum wave and crest heights,” Coastal Eng., 40, pp. 329–360.
Arena,  F., and Fedele,  F., 2002, “A family of narrow-band non-linear stochastic processes for the mechanics of sea waves,” Eur. J. Mech. B/Fluids, 21, pp. 125–137.
Al-Humoud,  J., Tayfun,  M. A., and Askar,  H., 2002, “Distribution of nonlinear wave crests,” Ocean Eng., 29, pp. 1929–1943.
Tayfun,  M. A., and Al-Humoud,  J., 2002, “Least upper bound distribution for nonlinear wave crest,” J. Waterw., Port, Coastal, Ocean Eng., 128(4), pp. 144–151.
Fedele,  F., Arena  F., 2004, “Weakly nonlinear statistics of high random waves,” Phys. Fluids, 17(2), pp. 1–10.

Figures

Grahic Jump Location
The second-order space–time evolution of a wave group in which a very large crest occurs at (X=0,T=to)
Grahic Jump Location
The second-order time evolution of a wave group in which a very large crest occurs. The solid lines give the second-order prediction [Eq. (38)]. The dotted line gives linear prediction [Eq. (6)], which is the “New wave” symmetric wave profile.
Grahic Jump Location
The time domain second-order wave pressure Δp at point (xo,z/Lp0=−0.05), when a very large crest height HC of free surface displacement occurs at (xo,T=0) (see Fig. 2). The solid lines give the second-order perdiction. The dotted line gives linear prediction.
Grahic Jump Location
The second-order time evolution of a wave group at fixed points X/Lp0, when a very large crest occurs at (X=0,T=0). The dotted lines show linear predictions, obtained from Boccotti’s quasi-determinism theory (first formulation).
Grahic Jump Location
The second-order time evolution of a wave group at fixed points X/Lp0(−0.20,−0.10,0,0.10,0.20) when a very large crest occurs at (X=0,T=0)
Grahic Jump Location
The second-order probability of exceeding the crest height, obtained both with presented model (continuous line) and with Forristall model (broken line). The dotted line gives the Rayleigh distribution (exact to the first-order). Data is obtained from numerical simulations.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In