On the nonlinear dynamics of wave groups produced by the focusing of surface-water waves

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2032, 2003, Pages 1021-1052

  Johannessen, T B ^a,b   Swan, C ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b Aker Kvaerner   (Norway)

Author keywords

Directional waves; Focused waves; Nonlinear waves; Rogue waves; Surface water waves; Wave groups

Indexed keywords

SURFACE WATER;

ACCURACY; ARTICLE; CALCULATION; FLOW RATE; HYDRODYNAMICS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONLINEAR SYSTEM; WAVEFORM;

EID: 1542512316     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1028     Document Type: Article

References (40)

1. Baldock, T. E., Swan, C. & Taylor, P. H. 1996 A laboratory study of nonlinear surface waves on water. Phil. Trans. R. Soc. Lond. A 354, 649-676.
2. Bateman, W. J. D. 2000 A numerical investigation of three-dimensional extreme water waves. PhD thesis, Imperial College, University of London, UK.
3. Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417-430.
4. Boccotti, P. 1983 Some new results on statistical properties of wind waves. Appl. Ocean Res. 5, 134-140.
5. Craig, W. & Sulem, C. 1993 Numerical simulation of gravity waves. J. Computat. Phys. 108, 73-83.
6. Dold, W. J. & Peregrine, D. H. 1984 Steep unsteady waves: an efficient computational scheme. In Proc. 19th Int. Conf. Coastal Engineering, ASCE, Houston, TX, vol. 1, pp. 955-967.
7. Dysthe, K. B. 1979 Note on the modification of the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105-114.
8. Fenton, J. D. & Rienecker, M. M. 1982 A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions. J. Fluid Mech. 118, 411-443.
9. Fox, M. J. H. 1976 On the nonlinear transfer of energy in the peak of a gravity-wave spectrum. Proc. R. Soc. Lond. A 348, 467-483.
10. Gear, C. W. 1971 Numerical initial value problems in ordinary differential equations. Englewood Cliffs, NJ: Prentice Hall.
11. Hammack, J. L. & Henderson, D. M. 1993 Resonant interactions among surface water waves. A. Rev. Fluid Mech. 25, 55-97.
12. Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481-500.
13. Hasselmann, K. 1963 On the nonlinear energy transfer in a gravity-wave spectrum. Part 2. Conservation theorems; waveparticle analogy; irreversibility. J. Fluid Mech. 15, 273-281.
14. Hasselmann, K. (and 15 others) 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutschen Hydrographischen Zeitschrift, Reihe A8, Nr. 12.
15. Henderson, K. L., Peregrine, D. H. & Dold, J. W. 1999 Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation. Wave Motion 29, 341-361.
16. James, R. L. & Swan, C. 2003 Applications of a fluid sheet model to combined waves and currents. Part 1. Equilibrium conditions. (Submitted.)
17. Johannessen, T. B. 1997 The effect of directionality on the nonlinear behaviour of extreme transient ocean waves. PhD thesis, University of London, UK.
18. Johannessen, T. B. & Swan, C. 1997 Nonlinear transient water waves. Part 1. A numerical method of computation with comparisons to 2-D laboratory data. Appl. Ocean Res. 19, 293-308.
19. Johannessen, T. B. & Swan, C. 1999 Steep transient wave events. In Proc. Int. Conf. Offshore Mech. and Artic Engineering (OMAE), St Johns, Newfoundland, OMAE99/S&R-6181. New York: ASME International.
20. Johannessen, T. B. & Swan, C. 2001 A laboratory study of the focusing of transient and directionally spread surface water waves. Proc. R. Soc. Lond. A 457, 971-1006.
21. Jonathan, P., Taylor, P. H. & Tromans, P. S. 1994 Storm waves in the northern North Sea. In Proc. 7th Int. Conf. Behaviour of Offshore Structures, MA, vol. 2, pp. 481-494.
22. Lindgren, G. 1970 Some properties of a normal process near a local maximum. Ann. Math. Statis. 41, 1870-1883.
23. Longuet-Higgins, M. S. 1963 The effects of nonlinearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, 459-480.
24. Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1-26.
25. Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8, 565-583.
26. Phillips, O. M. 1977 Dynamics of the upper ocean. Cambridge University Press.
27. Pierson, W. J. & Moskowitz, L. 1964 A proposed spectral form for fully developed wind seas based on the similarity laws of S. A. Kitaigorodskii. J. Geophys. Res. 69, 5181-5190.
28. Press, W., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1992 Numerical recipes in FORTRAN, 2nd edn. Cambridge University Press.
29. Priestley, M. B. 1994 Spectral analysis and time series. Academic.
30. Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735-800.
31. Sharma, J. N. & Dean, R. G. 1981 Second-order directional seas and associated wave forces. Soc. Petroleum Eng. J. 4, 129-140.
32. Skyner, D. 1996 A comparison of numerical predictions and experimental measurements of the internal kinematics of a deep-water plunging wave. J. Fluid Mech. 315, 51-64.
33. Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441-445.
34. Swan, C., Cummins, I. P. & James, R. L. 2001 An experimental study of two-dimensional surface water waves propagating on depth-varying currents. Part 1. Regular waves. J. Fluid Mech. 428, 273-304.
35. Taylor, P. H. & Haagsma, I. J. 1994 Focusing of steep wave groups on deep water. In Proc. Int. Symp. Waves - Physical and Numerical Modelling, IAHR, Vancouver, vol. 2, pp. 862-870.
36. Teles Da Silva, A. F. & Peregrine, D. H. 1988 Steep, steady surface water waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281-302.
37. Tromans, P. S., Anaturk, A. & Hagemeijer, P. 1991 A new model for the kinematics of large ocean waves-application as a design wave. In Proc. 1st Int. Offshore and Polar Engineering Conf., Edinburgh, vol. 3, pp. 64-71.
38. Whalin, R. W. 1972 Wave refraction theory in a convergence zone. In Proc. 13th Int. Conf. Coastal Engineering, ASCE, vol. 1, pp. 451-470.
39. Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 86-94.
40. Zakharov, V. E. & Shabat, A. B. 1972 Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 65, 997-1011.