Table of Contents
International Journal of Oceanography
Volume 2014, Article ID 597895, 9 pages
http://dx.doi.org/10.1155/2014/597895
Research Article

Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States

1Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700 009, India
2Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, Birbhum 731234, India

Received 14 February 2014; Accepted 2 May 2014; Published 9 June 2014

Academic Editor: Leonard Pietrafesa

Copyright © 2014 S. Debsarma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” European Journal of Mechanics B: Fluids, vol. 22, no. 6, pp. 603–634, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Toffoli, J. Monbaliu, J. M. Lefěvre, and E. Bitner-Gregersen, “Dangerous sea-states for marine operations,” in Proceedings of the 14th International Offshore and Polar Engineering Conference (ISOPE '04), pp. 85–92, Toulon,France, May 2004. View at Scopus
  3. K. B. Dysthe, “Modelling a “rogue wave”—speculations or a realistic possibility ?” in Proceedings of the Rogue Waves, M. Olagon and G. Athanassoulis, Eds., pp. 255–264, Ifremer, France, 2002.
  4. B. S. White and B. Fornberg, “On the chance of freak waves at sea,” Journal of Fluid Mechanics, vol. 355, pp. 113–138, 1998. View at Google Scholar · View at Scopus
  5. M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: a possible mechanism for the formation of freak waves,” Physical Review Letters, vol. 96, no. 1, Article ID 014503, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Physical Review Letters, vol. 97, no. 9, Article ID 094501, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. F. E. Laine-Pearson, “Instability growth rates of crossing sea states,” Physical Review E, vol. 81, Article ID 036316, pp. 1–7, 2010. View at Google Scholar
  8. K. B. Dysthe, “Note on a modification to the nonlinear Schrödinger equation for application to deep water waves,” Proceedings of the Royal Society of London A, vol. 369, pp. 105–114, 1979. View at Google Scholar
  9. O. Gramstad and K. Trulsen, “Fourth-order coupled nonlinear Schrödinger equations for gravity waves on deep water,” Physics of Fluids, vol. 23, no. 6, Article ID 062102, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. K. Trulsen and K. B. Dysthe, “A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water,” Wave Motion, vol. 24, no. 3, pp. 281–289, 1996. View at Publisher · View at Google Scholar · View at Scopus
  11. J. W. McLean, Y. C. Ma, D. U. Martin, P. G. Saffman, and H. C. Yuen, “Three-dimensional instability of finite-amplitude water waves,” Physical Review Letters, vol. 46, no. 13, pp. 817–820, 1981. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Debsarma and K. P. Das, “A higher-order nonlinear evolution equation for broader bandwidth gravity waves in deep water,” Physics of Fluids, vol. 17, no. 10, Article ID 104101, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. T. B. Benjamin and P. J. Olver, “A higher order nonlinear evolution equation for broader bandwidth gravity waves in deep water,” Journal of Fluid Mechanics, vol. 125, pp. 137–185, 1982. View at Google Scholar · View at Scopus
  14. V. E. Zakharov, “Stability of periodic waves of finite amplitude on the surface of a deep fluid,” Journal of Applied Mechanics and Technical Physics, vol. 9, no. 2, pp. 190–194, 1968. View at Publisher · View at Google Scholar · View at Scopus
  15. V. P. Krasitskii, “On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves,” Journal of Fluid Mechanics, vol. 272, pp. 1–21, 1994. View at Google Scholar · View at Scopus
  16. S. S. Debsarma and K. P. Das, “Fourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep water,” Physics of Fluids, vol. 19, no. 9, Article ID 097101, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Debsarma and K. P. Das, “A higher-order nonlinear evolution equation for broader bandwidth gravity waves in deep water,” Physics of Fluids, vol. 17, no. 10, Article ID 104101, 2005. View at Publisher · View at Google Scholar · View at Scopus