Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-01T02:45:12.406Z Has data issue: false hasContentIssue false
  • English
  • Français

On dispersion of directional surface gravity waves

Published online by Cambridge University Press:  05 January 2017

Tore Magnus A. Taklo ,
Karsten Trulsen ,
Harald E. Krogstad  and
José Carlos Nieto Borge
Tore Magnus A. Taklo
Affiliation:
Department of Mathematics, University of Oslo, Blindern, 0316 Oslo, Norway
Karsten Trulsen*
Affiliation:
Department of Mathematics, University of Oslo, Blindern, 0316 Oslo, Norway
Harald E. Krogstad
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
José Carlos Nieto Borge
Affiliation:
Department of Signal Theory and Communications, University of Alcalá, Plaza de San Diego, s/n, 28801 Alcalá de Henares, Madrid, Spain
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Using a nonlinear evolution equation we examine the dependence of the dispersion of directional surface gravity waves on the Benjamin–Feir index (BFI) and crest length. A parameter for describing the deviation between the dispersion of simulated waves and the theoretical linear dispersion relation is proposed. We find that for short crests the magnitude of the deviation parameter is low while for long crests the magnitude is high and depends on the BFI. In the present paper we also consider laboratory data of directional waves from the Marine Research Institute of the Netherlands (MARIN). The MARIN data confirm the simulations for three cases of BFI and crest length.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 681 - 697
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alber, I. A. 1978 The effects of randomness on the stability of two-dimensional surface wavetrains. Proc. R. Soc. Lond. A 363, 525–546.Google Scholar
Alber, I. E. & Saffman, P. G. 1978 Stability of random nonlinear deep water waves with finite bandwidth. In TWR Defense and Spacesystems Rep., 31326–6035–RU–00, 89.Google Scholar
Bateman, W. J. D., Swan, C. & Taylor, P. H. 2001 On the efficient numerical simulation of directionally-spread surface water waves. J. Comput. Phys. 174, 277–305.Google Scholar
Crawford, D. R., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion 2, 1–16.Google Scholar
Dysthe, K. B. 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Phil. Trans. R. Soc. Lond. A 369, 105–114.Google Scholar
Fessler, J. A. & Sutton, B. P. 2003 Nonuniform fast Fourier transform using min-max interpolation. IEEE Trans. Signal Process. 51, 560–574.Google Scholar
Gibson, R. S. & Swan, C. 2006 The evolution of large ocean waves: the role of local and rapid spectral changes. Proc. R. Soc. Lond. A 463, 21–48.Google Scholar
Goda, Y. 2000 Random Seas and Design of Maritime Structures. World Scientific.Google Scholar
Gramstad, O. & Trulsen, K. 2007 Influence of crest and group length on the occurence of freak waves. J. Fluid Mech. 582, 463–472.Google Scholar
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P. et al. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Erg. zur Deutsch. Hydrograph. Z. A 8 (12), 95.Google Scholar
Houtani, H., Waseda, T., Fujimoto, W., Kiyomatsu, K. & Tanizawa, K. 2015 Freak wave generation in a wave basin with HOSM-WG method. In ASME 2015 34th International Conference on Ocean, Offshore and Artic Engng, Paper no. OMAE2015-42284.Google Scholar
Janssen, P. A. E. M. 2003 Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884.Google Scholar
Krogstad, H. E. & Trulsen, K. 2010 Interpretations and observations of ocean wave spectra. Ocean Dyn. 60, 973–991.Google Scholar
Lo, E. & Mei, C. C. 1985 A numerical study of water-wave modulations based on a higher-order nonlinear Schrödinger equation. J. Fluid Mech. 150, 395–415.Google Scholar
Lo, E. & Mei, C. C. 1987 Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study. Wave Motion 9, 245–259.Google Scholar
Mori, N., Onorato, M. & Janssen, P. A. E. M. 2011 On the estimation of the kurtosis in directional sea states for freak wave forecasting. J. Phys. Oceanogr. 41, 1484–1497.Google Scholar
Naaijen, P., van Dijk, R., Huijsmans, R. H. M., El-Mouhandiz, A. A. & Danneberg, J. 2009 Real time estimation of ship motions in short crested seas. In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engng, Paper No. OMAE2009-79366, pp. 243–255.Google Scholar
Nieto Borge, J. C., Rodríguez, G., Hessner, K. & Izquierdo, P. 2004 Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean Technol. 21, 1291–1300.Google Scholar
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834.Google Scholar
Simanesew, A., Krogstad, H. E., Trulsen, K. & Nieto Borge, J. C. 2016 Development of frequency-dependent ocean wave directional distributions. Appl. Ocean Res. 59, 304–312.Google Scholar
Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H. E. & Liu, J. D. 2005 Probability distributions of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195–216.Google Scholar
Taklo, T. M. A., Trulsen, K., Gramstad, O., Krogstad, H. E. & Jensen, A. 2015 Measurement of the dispersion relation for random surface gravity waves. J. Fluid Mech. 766, 326–336.Google Scholar
Toffoli, A., Gramstad, O., Trulsen, K., Monbaliu, J., Bitner-Gregersen, E. & Onorato, M. 2010 Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations. J. Fluid Mech. 664, 313–336.Google Scholar
Trulsen, K., Kliakhandler, I., Dysthe, K. B. & Velarde, M. G. 2000 On weakly nonlinear modulation of waves on deep water. Phys. Fluids 12, 2432–2437.Google Scholar
Tucker, M. J. & Pitt, E. G. 2001 Waves in Ocean Engineering. Elsevier.Google Scholar
Waseda, T., Kinoshita, T. & Tamura, H. 2009 Evolution of a random directional wave and freak wave occurence. J. Phys. Oceanogr. 39, 621–639.Google Scholar
Xiao, W., Liu, Y., Wu, G. & Yue, D. K. P. 2013 Rouge wave occurence and dynamics by direct simulations of nonlinear wave-field evolution. J. Fluid Mech. 720, 357–392.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.CrossRefGoogle Scholar