Qualitative comparisons of experimental results on deterministic freak wave generation based on modulational instability

Journal of Hydro-Environment Research

Volumn 3, Issue 4, 2010, Pages 186-192

  Karjanto, N ^a   van Groesen, E ^b,c  

^a UNIVERSITY OF NOTTINGHAM MALAYSIA CAMPUS   (Malaysia)

^b UNIVERSITY OF TWENTE   (Netherlands)

^c LabMath Indonesia   (Indonesia)

Author keywords

Freak wave generation; Frequency downshift; Modulational instability; Nonlinear Schr dinger equation; Phase singularity; Soliton on Finite Background; Wessel curve

Indexed keywords

CARRIER WAVES; DINGER EQUATION; EXACT SOLUTION; FREAK WAVE; FREQUENCY DOWNSHIFT; MODULATION PERIOD; MODULATIONAL INSTABILITY; NONLINEAR DISPERSIVE; PHASE SINGULARITIES; THEORETICAL MODELS;

EXPERIMENTS; SOLITONS; STABILITY; WAVE EQUATIONS;

NONLINEAR EQUATIONS;

HYDRODYNAMICS; NUMERICAL MODEL; OCEAN WAVE; WAVE GENERATION;

EID: 77949300807     PISSN: 15706443     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jher.2009.10.008     Document Type: Article

References (32)

1. Ablowitz M.J., and Herbst B.M. On homoclinic structure and numerically induced chaos for the nonlinear schrödinger equation. SIAM J. Appl. Math. 50 2 (1990) 339-351
2. Akhmediev N.N., and Ankiewicz A. Solitons-Nonlinear Pulses and Beams. Optical and Quantum Electronic Series. first ed vol. 5 (1997), Chapman & Hall
3. Akhmediev N.N., Eleonskiǐ V.M., and Kulagin N.E. Teoret. Mat. Fiz. 72 2 (1987) 183-196 English translation: Theoret. Math. Phys. 72(2): 809-818, 1987
4. Andonowati, Karjanto N., and van Groesen E. Extreme wave phenomena in down-stream running modulated waves. Appl. Math. Model. 31 7 (2007) 1425-1443
5. Argand R. Essai sur une manière de représenter les quantités imag-inaires dans les constructions géométriques (1806) Paris
6. Benjamin T.B., and Feir J.E. The disintegration of wave trains in deep water. J. Fluid Mech. 27 (1967) 417-430
7. Dysthe K.B., and Trulsen K. Note on breather type solutions of the NLS as models for freak-waves. Phys. Scripta T82 (1999) 48-52
8. Dysthe K.B. Note on a modification to the nonlinear schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369 (1979) 105-114
9. Hara T., and Mei C.C. Frequency downshift in narrowbanded surface waves under the influence of wind. J. Fluid Mech. 230 (1991) 429-477
10. Hasselmann K., et al. Measurements of wind wave growth and swell decay during the Joint North Sea Wave Project. Herausgegeben vom Deutsch. Hydrogr. Institut. A 12 (1973) 95
11. Henderson K.L., Peregrine D.H., and Dold J.W. Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation. Wave Motion 29 (1999) 341-361
12. Huijsmans R.H.M., Klopman G., Karjanto N., and Andonowati. Experiments on extreme wave generation using the Soliton on Finite Background. In: Olagnon M., and Prevosto M. (Eds). Rogue Waves 2004, Workshop Proceedings, Brest, France (2005) 10
13. Janssen P.A.E.M. Nonlinear four-wave interactions and freak waves. J. Phys. Ocean. 33 (2003) 863-884
14. Karjanto N., and van Groesen E. Note on wavefront dislocation in surface water waves. Phys. Lett. A 371 3 (2007) 173-179
15. Karjanto, N., 2006. Mathematical aspects of extreme water waves. PhD thesis, University of Twente, The Netherlands.
16. Kato Y., and Oikawa M. Wave number downshift in modulated wave-train through a nonlinear damping effect. J. Phys. Soc. Japan 64 12 (1995) 4660-4669
17. Lake B.M., Yuen H.C., Rundgaldier H., and Ferguson W.E. Nonlinear deep water waves: theory and experiment. Part 2. Evolution of a continous wave train. J. Fluid Mech. 83 (1977) 49-74
18. Lo E., and Mei C.C. A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation. J. Fluid Mech. 150 (1985) 395-416
19. Mei C.C., Stiassnie M., and Yue D.K.P. Theory and Applications of Ocean Surface Waves, Part 2: Nonlinear Aspects. Advanced Series on Ocean Engineering vol. 23 (2005), World Scientific, Singapore
20. Melville W.K. The instability and breaking of deep-water waves. J. Fluid Mech. 115 (1982) 165-185
21. Onorato M., Osborne A.R., Serio M., and Bertone S. Freak waves in random oceanic sea states. Phys. Rev. Lett. 86 (2001) 5831-5834
22. Osborne A.R., Onorato M., and Serio M. The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains. Phys. Lett. A 275 (2000) 386-393
23. Osborne A.R. The random and deterministic dynamics of 'rogue waves' in unidirectional, deep-water wave trains. Mar. Struct. 14 (2001) 275-293
24. Pierson W.J., Neuman G., and James R.W. Practical Methods for Observing and Forecasting Ocean Waves By Means of Wave Spectra and Statistics (1958), Hydrographic Office, US Navy
25. The Internet Encyclopedia of Science.
26. Trulsen K., and Dysthe K.B. A modified nonlinear Schrödinger equation for broader bandwith gravity waves on deep water. Wave Motion 24 (1996) 281-289
27. Trulsen K., and Dysthe K.B. Frequency downshift in three-dimensional wave trains in a deep basin. J. Fluid Mech. 352 (1997) 359-373
28. Trulsen K., Stansberg C.T., and Velarde M.G. Laboratory evidence of three-dimensional frequency downshift of waves in a long tank. Phys. Fluids 11 1 (1999) 235-237
29. Van Groesen E., and Andonowati. Variational derivation of KdV-type models for surface water waves. Phys. Lett. A 366 (2007) 195-201
30. Van Groesen, E., Andonowati, She Liam, L., Lakthturov, I. Accurate modelling of uni-directional surface waves, J. Comput. Appl. Math., in press, doi:10.1016/j.cam.2009.08.024.
31. Van Groesen E. Wave groups in uni-directional surface-wave model. J. Eng. Math. 34 1-2 (1998) 215-226
32. Yuen H.C., and Lake B.M. Nonlinear dynamics of deep water gravity waves. Adv. Appl. Mech. 22 (1982) 67-229