• Banner, M. L., and W. L. Peirson, 2007: Wave breaking onset and strength for two-dimensional deep-water wave groups. J. Fluid Mech., 585 , 93115.

    • Search Google Scholar
    • Export Citation
  • Bendat, J. S., and A. G. Piersol, 1986: Random Data. 2nd ed. John Wiley & Sons, 566 pp.

  • Benjamin, T. B., and J. E. Feir, 1967: The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech., 27 , 417430.

  • Brown, E. D., S. B. Buchsbaum, R. E. Hall, J. P. Penhune, K. F. Schmitt, K. M. Watson, and D. C. Wyatt, 1989: Observations of a nonlinear solitary wave packet in the Kelvin wake of a ship. J. Fluid Mech., 204 , 263293.

    • Search Google Scholar
    • Export Citation
  • Crawford, C. B., and D. M. Farmer, 1987: On the spatial distribution of ocean bubbles. J. Geophys. Res., 92 , 82318243.

  • Dysthe, K., 1979: Note on a modification to the non-linear Schrodinger-equation for application to deep-water waves. Proc. Roy. Soc. London, 369A , 105114.

    • Search Google Scholar
    • Export Citation
  • Dysthe, K., H. E. Krogstad, and P. Muller, 2008: Oceanic rogue waves. Annu. Rev. Fluid Mech., 40 , 287310.

  • Hasselmann, K., and Coauthors, 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogr. Z., 80 , (Suppl. A). 195.

    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., R. Pinkel, and L. Rainville, 2008: Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr., 38 , 380399.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1978: Instabilities of gravity-waves of finite-amplitude in deep water. 2. Subharmonics. Proc. Roy. Soc. London, 360A , 489505.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., and R. W. Stewart, 1962: Radiation stress and mass transport in gravity waves, with application to ‘surf-beats’. J. Fluid Mech., 13 , 481504.

    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1958: The equilibrium range in the spectrum of wind-generated ocean waves. J. Fluid Mech., 4 , 426434.

  • Pinkel, R., and J. A. Smith, 1992: Repeat-sequence coding for improved precision of Doppler sonar and sodar. J. Atmos. Oceanic Technol., 9 , 149163.

    • Search Google Scholar
    • Export Citation
  • Pinkel, R., and D. Rudnick, 2006: Hawaii Ocean Mixing Experiment (HOME). J. Phys. Oceanogr., 36 , 965966.

  • Rummler, W. D., 1968: Introduction of a new estimator for velocity spectral parameters. AT&T Bell Labs. Rep. MM-68-4141-5, 24 pp.

  • Smith, J. A., 2002: Continuous time–space sampling of near-surface velocities using sound. J. Atmos. Oceanic Technol., 19 , 18601872.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 2006a: Wave–current interactions in finite depth. J. Phys. Oceanogr., 36 , 14031419.

  • Smith, J. A., 2006b: Observed variability of ocean wave stokes drift, and the Eulerian response to passing groups. J. Phys. Oceanogr., 36 , 13811402.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 2008: Vorticity and divergence of surface velocities near shore. J. Phys. Oceanogr., 38 , 14501468.

  • Smith, J. A., and R. Pinkel, 1991: Improvement of Doppler estimation through repeat sequence coding. Proc. Oceans ‘91: USA/Ocean Technologies and Opportunities in the Pacific for the 90’s, Honolulu, HI, Institute of Electrical and Electronics Engineers, 977–984.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., and G. T. Bullard, 1995: Directional surface wave estimates from Doppler sonar data. J. Atmos. Oceanic Technol., 12 , 617632.

    • Search Google Scholar
    • Export Citation
  • Stokes, G. G., 1847: On the theory of oscillatory waves. Trans. Cambridge Philos. Soc., 8 , 441455.

  • Thorpe, S. A., 1986: Bubble clouds: A review of their detection by sonar, of related models, and of how Kv may be determined. Oceanic Whitecaps and Their Role in Air–Sea Exchange Processes, E. C. Monahan and G. Mac Niocaill, Eds., Springer, 57–68.

    • Search Google Scholar
    • Export Citation
  • Tulin, M. P., and T. Waseda, 1999: Laboratory observations of wave group evolution, including breaking effects. J. Fluid Mech., 378 , 197232.

    • Search Google Scholar
    • Export Citation
  • Whitham, G. B., 1974: Linear and Nonlinear Waves. Wiley-Interscience, 636 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 57 34 0
PDF Downloads 36 20 0

Evolution of Persistent Wave Groups

View More View Less
  • 1 Scripps Institution of Oceanography, La Jolla, California
  • | 2 Institut des Sciences de l’Ingénieur Toulon Var, Toulon, France
Restricted access

Abstract

During the near-field leg of the Hawaiian Ocean-Mixing Experiment (HOME-NF), short, steep surface wave groups were observed that elicited strong group-forced responses in the wave-filtered surface current field, as reported by Smith. Some of these wave groups persisted for 17 wave periods, yet were only about 1 wavelength long in the along-wind direction. Here, the authors consider the evolution of wave groups of the form observed and find that this persistence is consistent with linear dispersion in spite of the very compact form. The key aspects enhancing persistence are 1) that the wave crests within the group are oriented at an angle with respect to the group envelope and 2) they are much wider in the crosswind direction than along-wind (in the example examined in detail, about 5 times). According to a simplified model, groups with the observed 5-to-1 aspect ratio and this “slant-wave” structure can persist for up to 20 wave periods, consistent with the observations (cf. 8 periods for a collinear wave group). The maximum persistence increases in proportion to the across-wind length of the group.

Corresponding author address: Dr. Jerome A. Smith, Mail Code 0213, 9500 Gilman Dr., La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

Abstract

During the near-field leg of the Hawaiian Ocean-Mixing Experiment (HOME-NF), short, steep surface wave groups were observed that elicited strong group-forced responses in the wave-filtered surface current field, as reported by Smith. Some of these wave groups persisted for 17 wave periods, yet were only about 1 wavelength long in the along-wind direction. Here, the authors consider the evolution of wave groups of the form observed and find that this persistence is consistent with linear dispersion in spite of the very compact form. The key aspects enhancing persistence are 1) that the wave crests within the group are oriented at an angle with respect to the group envelope and 2) they are much wider in the crosswind direction than along-wind (in the example examined in detail, about 5 times). According to a simplified model, groups with the observed 5-to-1 aspect ratio and this “slant-wave” structure can persist for up to 20 wave periods, consistent with the observations (cf. 8 periods for a collinear wave group). The maximum persistence increases in proportion to the across-wind length of the group.

Corresponding author address: Dr. Jerome A. Smith, Mail Code 0213, 9500 Gilman Dr., La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

Save