• Annenkov, S. Y., and V. I. Shrira, 2006: Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech., 561, 181207, doi:10.1017/S0022112006000632.

    • Search Google Scholar
    • Export Citation
  • Ardhuin, F., W. C. O’Reilly, T. H. C. Herbers, and P. F. Jessen, 2003: Swell transformation across the continental shelf. Part I: Attenuation and directional broadening. J. Phys. Oceanogr., 33, 19211939, doi:10.1175/1520-0485(2003)033<1921:STATCS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ardhuin, F., and Coauthors, 2012: Numerical wave modeling in conditions with strong currents: Dissipation, refraction, and relative wind. J. Phys. Oceanogr., 42, 21012120, doi:10.1175/JPO-D-11-0220.1.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., and Y. P. Soloviev, 1998: Variability of directional spectra of wind-generated waves, studied by means of wave staff arrays. Mar. Freshwater Res., 49, 89101, doi:10.1071/MF96126.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., H. Hwung, I. Shugan, A. Roland, A. V. der Westhuysen, A. Chawla, and C. Gautier, 2011: Nonlinear waves on collinear currents with horizontal velocity gradient. Proc. 12th Int. Workshop on Wave Hindcasting and Forecasting and Third Coastal Hazards Symp., Kohala Coast, Hawaii, Wave Workshop, 1–24. [Available online at http://www.waveworkshop.org/12thWaves/papers/Babanin_et_al_2011_Hawaii_submitted.pdf.]

  • Benjamin, T. B., and J. E. Feir, 1967: The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech., 27, 417430, doi:10.1017/S002211206700045X.

    • Search Google Scholar
    • Export Citation
  • Benney, D. J., 1962: Non-linear gravity wave interactions. J. Fluid Mech., 14, 577584, doi:10.1017/S0022112062001469.

  • Chawla, A., and J. T. Kirby, 2002: Monochromatic and random wave breaking at blocking points. J. Geophys. Res., 107, doi:10.1029/2001JC001042.

    • Search Google Scholar
    • Export Citation
  • Donelan, M., W. M. Drennan, and A. K. Magnusson, 1996: Nonstationary analysis of the directional properties of propagating waves. J. Phys. Oceanogr., 26, 19011914, doi:10.1175/1520-0485(1996)026<1901:NAOTDP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gramstad, O., and A. V. Babanin, 2016: The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models. Ocean Dyn., 66, 509526, doi:10.1007/s10236-016-0940-4.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1962: On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech., 12, 481500, doi:10.1017/S0022112062000373.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., and Coauthors, 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Waves Project (JONSWAP). Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift 12, 95 pp.

  • Haus, B. K., 2007: Surface current effects on the fetch-limited growth of wave energy. J. Geophys. Res., 112, C03003, doi:10.1029/2006JC003924.

    • Search Google Scholar
    • Export Citation
  • Janssen, P. A. E. M., 2003: Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr., 33, 863884, doi:10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kenyon, K. E., 1971: Wave refraction in ocean currents. Deep-Sea Res. Oceanogr. Abstr., 18, 10231034, doi:10.1016/0011-7471(71)90006-4.

    • Search Google Scholar
    • Export Citation
  • Krasitskii, V. P., 1994: On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech., 272, 120, doi:10.1017/S0022112094004350.

    • Search Google Scholar
    • Export Citation
  • Lai, R. J., S. R. Long, and N. E. Huang, 1989: Laboratory studies of wave-current interaction: Kinematics of the strong interaction. J. Geophys. Res., 94, 16 20116 214, doi:10.1029/JC094iC11p16201.

    • Search Google Scholar
    • Export Citation
  • Long, R. B., 1973: Scattering surface of waves an irregular by bottom. J. Geophys. Res., 78, 78617870, doi:10.1029/JC078i033p07861.

  • Longuet-Higgins, M. S., 1962: Resonant interactions between two trains of gravity waves. J. Fluid Mech., 12, 321332, doi:10.1017/S0022112062000233.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., and R. W. Stewart, 1961: The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech., 10, 529549, doi:10.1017/S0022112061000342.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., and O. M. Phillips, 1962: Phase velocity effects in tertiary wave-interactions. J. Fluid Mech., 12, 333336, doi:10.1017/S0022112062000245.

    • Search Google Scholar
    • Export Citation
  • Mitsuyasu, H., F. Tasai, T. Suhara, S. Mizuno, M. Ohkusu, T. Honda, and K. Rikiishi, 1975: Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanogr., 5, 750759, doi:10.1175/1520-0485(1975)005<0750:OOTDSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Moreira, R. M., and D. H. Peregrine, 2012: Nonlinear interactions between deep-water waves and currents. J. Fluid Mech., 691, 125, doi:10.1017/jfm.2011.436.

    • Search Google Scholar
    • Export Citation
  • Mori, N., M. Onorato, and P. A. E. M. Jansen, 2011: On the estimation of the kurtosis in directional sea states for freak wave forecasting. J. Phys. Oceanogr., 41, 14841497, doi:10.1175/2011JPO4542.1.

    • Search Google Scholar
    • Export Citation
  • Onorato, M., A. Osborne, M. Serio, L. Cavaleri, C. Brandini, and C. Stansberg, 2004: Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments. Phys. Rev., 70, 067302, doi:10.1103/PhysRevE.70.067302.

    • Search Google Scholar
    • Export Citation
  • Onorato, M., D. Proment, and A. Toffoli, 2011: Triggering rogue waves in opposing currents. Phys. Rev. Lett., 107, 184502, doi:10.1103/PhysRevLett.107.184502.

    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1960: On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech., 9, 193217, doi:10.1017/S0022112060001043.

    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1977: The Dynamics of the Upper Ocean. Cambridge University Press, 336 pp.

  • Qingpu, Z., 1996: Nonlinear instability of wavetrain under influences of shear current with varying vorticity and air pressure. Acta Mech. Sin., 12, 2438, doi:10.1007/BF02486759.

    • Search Google Scholar
    • Export Citation
  • Rapizo, H., A. Babanin, O. Gramstad, and M. Ghantous, 2014: Wave refraction on Southern Ocean eddies. Proc. 19th Australasian Fluid Mechanics Conf., Melbourne, Australia, Australian Fluid Mechanics Society, 1–4. [Available online at http://people.eng.unimelb.edu.au/imarusic/proceedings/19/18.pdf.]

  • Ribal, A., A. V. Babanin, I. R. Young, A. Toffoli, and M. Stiassnie, 2013: Recurrent solutions of the Alber equation initialized by Joint North Sea Wave Project spectra. J. Fluid Mech., 719, 314344, doi:10.1017/jfm.2013.7.

    • Search Google Scholar
    • Export Citation
  • Stewart, R. H., and J. W. Joy, 1974: HF radio measurements of surface currents. Deep-Sea Res. Oceanogr. Abstr., 21, 10391049, doi:10.1016/0011-7471(74)90066-7.

    • Search Google Scholar
    • Export Citation
  • Takahashi, S., 2011: Particle motions of nonlinear water waves (in Japanese). M.S. thesis, University of Tokyo, Graduate School of Frontier Sciences, Japan, 83 pp.

  • Tamura, H., T. Waseda, Y. Miyazawa, and K. Komatsu, 2008: Current-induced modulation of the ocean wave spectrum and the role of nonlinear energy transfer. J. Phys. Oceanogr., 38, 26622684, doi:10.1175/2008JPO4000.1.

    • Search Google Scholar
    • Export Citation
  • Tanaka, M., 2001: Verification of Hasselmann’s energy transfer among surface gravity waves by direct numerical simulations of primitive equations. J. Fluid Mech., 444, 199221, doi:10.1017/S0022112001005389.

    • Search Google Scholar
    • Export Citation
  • Toffoli, A., and Coauthors, 2011: Occurrence of extreme waves in three-dimensional mechanically generated wave fields propagating over an oblique current. Nat. Hazards Earth Syst. Sci., 11, 895903, doi:10.5194/nhess-11-895-2011.

    • Search Google Scholar
    • Export Citation
  • Toffoli, A., T. Waseda, H. Houtani, T. Kinoshita, K. Collins, D. Proment, and M. Onorato, 2013: Excitation of rogue waves in a variable medium: An experimental study on the interaction of water waves and currents. Phys. Rev., 87, 051201, doi:10.1103/PhysRevE.87.051201.

    • Search Google Scholar
    • Export Citation
  • Toffoli, A., T. Waseda, H. Houtani, L. Caveleri, D. Greaves, and M. Onorato, 2015: Rogue waves in opposing currents: An experimental study on deterministic and stochastic wave trains. J. Fluid Mech., 769, 277297, doi:10.1017/jfm.2015.132.

    • Search Google Scholar
    • Export Citation
  • Trulsen, G. N., K. B. Dysthe, and J. Trulsen, 1990: Evolution of a gravity wave spectrum through a current gradient. J. Geophys. Res., 95, 22 14122 151, doi:10.1029/JC095iC12p22141.

    • Search Google Scholar
    • Export Citation
  • Waseda, T., T. Kinoshita, and H. Tamura, 2009a: Evolution of a random directional wave and freak wave occurrence. J. Phys. Oceanogr., 39, 621639, doi:10.1175/2008JPO4031.1.

    • Search Google Scholar
    • Export Citation
  • Waseda, T., T. Kinoshita, and H. Tamura, 2009b: Interplay of resonant and quasi-resonant interaction of the directional ocean waves. J. Phys. Oceanogr., 39, 23512362, doi:10.1175/2009JPO4147.1.

    • Search Google Scholar
    • Export Citation
  • Waseda, T., T. Kinoshita, L. Cavaleri, and A. Toffoli, 2015: Third-order resonant wave interactions under the influence of background current fields. J. Fluid Mech., 784, 5173, doi:10.1017/jfm.2015.578.

    • Search Google Scholar
    • Export Citation
  • White, B., and B. Fornberg, 1998: On the chance of freak waves at sea. J. Fluid Mech., 355, 113138, doi:10.1017/S0022112097007751.

  • Young, I. R., and G. Van Vleder, 1993: A review of the central role of nonlinear interactions in wind–wave evolution. Philos. Trans. Roy. Soc. London, 342, 505524, doi:10.1098/rsta.1993.0030.

    • Search Google Scholar
    • Export Citation
  • Yuen, H. C., and W. E. Ferguson, 1982: Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech., 22, 67229, doi:10.1016/S0065-2156(08)70066-8.

    • Search Google Scholar
    • Export Citation
  • Zakharov, V. E., 1968: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9, 190194, doi:10.1007/BF00913182.

    • Search Google Scholar
    • Export Citation
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Laboratory Experiments on the Effects of a Variable Current Field on the Spectral Geometry of Water Waves

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  • 1 Swinburne University of Technology, Hawthorn, Victoria, Australia
  • | 2 Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba, Japan
  • | 3 Swinburne University of Technology, Hawthorn, Victoria, Australia
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Abstract

Laboratory experiments were performed to investigate the effects of a coflowing current field on the spectral shape of water waves. The results indicate that refraction is the main factor in modulating wave height and overall wave energy. Although the structure of the current field varies considerably, some current-induced patterns in the wave spectrum are observed. In high frequencies, the energy cascading generated by nonlinear interactions is suppressed, and the development of a spectral tail is disturbed, as a consequence of the detuning of the four-wave resonance conditions. Furthermore, the presence of currents slows the downshifting of the spectral peak. The suppression of the high-frequency energy under the influence of currents is more prominent as the spectral steepness increases. The energy suppression is also more accentuated and long-standing along the fetch when the directional spreading of waves is sufficiently broad. This result indicates that the current-induced detuning of resonant conditions is more effective when exact resonances are the primary mechanism of nonlinear interactions than when quasi resonances prevail (directionally narrow cases). Additionally, the directional analysis shows that the highly variable currents broaden the directional spreading of waves. The broadening is suggested to be related to random refraction and scattering of wave rays. The random disturbance of wavenumbers alters the nonlinear interaction conditions and weakens the energy exchanges among wave components, which is expressed in the suppression of the high-frequency energy.

Current affiliation: University of Melbourne, Melbourne, Victoria, Australia.

Corresponding author address: Henrique Rapizo, Centre for Ocean Engineering, Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia. E-mail: hrapizo@swin.edu.au

Abstract

Laboratory experiments were performed to investigate the effects of a coflowing current field on the spectral shape of water waves. The results indicate that refraction is the main factor in modulating wave height and overall wave energy. Although the structure of the current field varies considerably, some current-induced patterns in the wave spectrum are observed. In high frequencies, the energy cascading generated by nonlinear interactions is suppressed, and the development of a spectral tail is disturbed, as a consequence of the detuning of the four-wave resonance conditions. Furthermore, the presence of currents slows the downshifting of the spectral peak. The suppression of the high-frequency energy under the influence of currents is more prominent as the spectral steepness increases. The energy suppression is also more accentuated and long-standing along the fetch when the directional spreading of waves is sufficiently broad. This result indicates that the current-induced detuning of resonant conditions is more effective when exact resonances are the primary mechanism of nonlinear interactions than when quasi resonances prevail (directionally narrow cases). Additionally, the directional analysis shows that the highly variable currents broaden the directional spreading of waves. The broadening is suggested to be related to random refraction and scattering of wave rays. The random disturbance of wavenumbers alters the nonlinear interaction conditions and weakens the energy exchanges among wave components, which is expressed in the suppression of the high-frequency energy.

Current affiliation: University of Melbourne, Melbourne, Victoria, Australia.

Corresponding author address: Henrique Rapizo, Centre for Ocean Engineering, Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia. E-mail: hrapizo@swin.edu.au
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