, Volume 57, Issue 2, pp 253–264 | Cite as

On the possibility of biphase parametrization for wave transformation in the coastal zone

  • Ya. V. Saprykina
  • M. N. Shtremel
  • S. Yu. Kuznetsov
Marine Physics


Based on experimental data, we study the possibility of parametrizing the spatial variation in the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over an inclined bottom in the coastal zone. It is revealed that the biphase values vary in the range [–π/2, π/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. Wave breaking influences the biphase value, retaining its variations in the negative domain in the range [–π/2, 0]. The formula applied in modern practice to calculate the biphase, which depends on the Ursell number, is incorrect for calculating the biphase for wave evolution in the coastal zone, because it does not take into account periodic energy exchange between the nonlinear harmonics. We propose a linear approximation of the biphase values from the size of the ratio of the current distance to the coast to the possible spacial duration of the exchange period, which is determined by the dispersion relation. We reveal the dependence of biphase variations on the wave transformation scenario and demonstrate the possibility of constructing a separate parameterization of the biphase for each scenario. Our research and the obtained biphase parameterizations can be used to simulate the sea state in the coastal zone, as well as in problems of predicting the development of coasts under the impact of storm waves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Glossary to Coastal (Offshore) Zone, Ed. by G. G. Gogoberidze, (Russian State Hydrometeorological Inst., St. Petersburg, 2008) [in Russian].Google Scholar
  2. 2.
    S. Yu. Kuznetsov and Ya. V. Saprykina, “Frequencydependent energy dissipation of irregular breaking waves,” Water Resour. 31 (4), 384–392 (2004).CrossRefGoogle Scholar
  3. 3.
    I. O. Leont’ev, Coastal Dynamics: Waves, Currents, and Alluvium Flows (GEOS, Moscow, 2001) [in Russian].Google Scholar
  4. 4.
    Ya. V. Saprykina, S. Yu. Kuznetsov, N. K. Andreeva, and M. N. Shtremel, “Scenarios of nonlinear wave transformation in the coastal zone,” Oceanology (Engl. Transl.) 53 (4), 422–431 (2013).Google Scholar
  5. 5.
    Ya. V. Saprykina, S. Yu. Kuznetsov, Zh. Cherneva, and N. Andreeva, “Spatio-temporal variability of the amplitude-phase structure of storm waves in the coastal zone of the sea,” Oceanology (Engl. Transl.) 49 (2), 182–192 (2009).Google Scholar
  6. 6.
    Ya. V. Saprykina, S. Yu. Kuznetsov, M. N. Shtremel, and V. Sundar, “Evaluation of the coastal zone vulnerability affected by waving at the southern coast zone of Hindustan Peninsula,” in The Processes in Geological Environments (Institute of Mechanics, Russian Academy of Sciences, Moscow, 2015), No. 3, pp. 76–88.Google Scholar
  7. 7.
    J. W. Daily and D. R. F. Harleman, Fluid Dynamics (Addison-Wesley, Reading, MA, 1966).Google Scholar
  8. 8.
    S. M. Antsyferov, R. D. Kosyan, S. Yu. Kuznetsov, and Ya. V. Saprykina, “Physical grounds for the formation of the sediment flux in the coastal zone of a nontidal sea,” Oceanology (Engl. Transl.) 45 (1), S183–S190 (2005).Google Scholar
  9. 9.
    R. A. Bagnold, “An approach to the sediment transport problem from general physics,” in US Geological Survey, Professional Paper (Washington, DC, 1966), No. 422_I.Google Scholar
  10. 10.
    J. A. Bailard and D. L. Inman, “An energetic bedload model for a plane sloping beach: Local transport,” J. Geophys. Res. 86, 2035–2043 (1981).CrossRefGoogle Scholar
  11. 11.
    J. A. Battjes and J. P. F. M. Janssen, “Energy loss and set-up due to breaking of random waves,” Proceedings of 16th Conf. on Coastal Engineering (Hamburg, 1978), pp. 569–587.Google Scholar
  12. 12.
    J. C. Doering and A. J. Bowen, “Shoaling surface gravity waves: a bispectral analysis,” Proceedings of 20th Conf. on Coastal Engineering, Taipei (American Society of Civil Engineers, Reston, WV, 1986), pp. 150–162.Google Scholar
  13. 13.
    J. C. Doering and A. J. Bowen, “Parametrization of orbital velocity asymmetries of shoaling and breaking waves using bispectral analysis,” Coastal Eng., No. 26, 15–33 (1995).CrossRefGoogle Scholar
  14. 14.
    Y. Eldeberky, “Nonlinear transformation of wave spectra in the nearshore zone,” in Communication on Hydraulic and Geotechnical Engineering, Report No. 96-4 (Technical University of Delft, Delft, 1996).Google Scholar
  15. 15.
    Y. Eldeberky and J. Battjes, “Parametrization of triad interactions in wave energy models,” Proceedings of the International Conf. on Coastal Research in Terms of Large Scale Experiments “Coastal Dynamics’95,” Gdansk (American Society of Civil Engineers, Reston, WV, 1995), pp. 140–148.Google Scholar
  16. 16.
    Y. Eldeberky and P. A. Madsen, “Determenistic and stochastic evolution equations for fully dispersive and weakly nonlinear waves,” Coastal Eng. 38, 1–24 (1999).CrossRefGoogle Scholar
  17. 17.
    S. Elgar and R. T. Guza, “Observation of bispectra of shoaling surface gravity waves,” J. Fluid Mech. 161, 425–448 (1985).CrossRefGoogle Scholar
  18. 18.
    S. Elgar and R. T. Guza, “Nonlinear model predictions of bispectra of shoaling surface gravity waves,” J. Fluid Mech. 167, 1–18 (1986).CrossRefGoogle Scholar
  19. 19.
    S. Elgar and R. T. Guza, “Shoaling gravity waves: comparison between field observations, linear theory and a nonlinear model,” J. Fluid Mech. 158, 47–70 (1985).CrossRefGoogle Scholar
  20. 20.
    K. Hasselmann, W. Munk, and G. MacDonald, “Bispectra of ocean waves,” Proceedings of the Symp. on Time Series Analysis (Wiley, New York, 1963), pp. 125–139.Google Scholar
  21. 21.
    Y. Kim and E. Powers, “Digital bispectral analysis and its application to non-linear wave interaction,” IEEE Trans. Plasma Sci. 1, 120–131 (1979).CrossRefGoogle Scholar
  22. 22.
    P. A. Madsen and O. R. Sorensen, “Bound waves and triad interactions in shallow water,” J. Ocean Eng. 20 (4), 359–388 (1993).CrossRefGoogle Scholar
  23. 23.
    SWAN, Technical documentation, 2006. http://www. Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  • Ya. V. Saprykina
    • 1
  • M. N. Shtremel
    • 1
  • S. Yu. Kuznetsov
    • 1
  1. 1.Shirshov Institute of OceanologyRussian Academy of SciencesMoscowRussia

Personalised recommendations