PARAMETERIZATION OF EVOLUTION OF BIPHASE DURING NONLINEAR TRANSFORMATION OF WAVES IN COASTAL ZONE
AbstractBased on experimental data, the problem of parametrization of spatial variation of the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over sloping bottom in the coastal zone is discussed. It is revealed that the biphase values vary in the range [-Ï€/2, Ï€/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. The empirical relation 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. The new approximations of the biphase values for typical scenarios of wave transformations are suggested. It was demonstrated that the biphase of breaking waves defines breaking index and breaking type.
Antsyferov S. M., R. D. Kosyan, S. Yu. Kuznetsov, and Ya. V. Saprykina. 2005. Physical grounds for the formation of the sediment flux in the coastal zone of a nontidal sea, Oceanology 45 (1), S183-S190.
Bagnold R. A. 1966. An approach to the sediment transport problem from general physics, US Geological Survey, Professional Paper, No. 422_I.
Bailard J. A. and D. L. Inman. 1981. An energetic bedload model for a plane sloping beach: Local transport, J. Geophys. Res. 86, 2035-2043.
Doering J. C. and A. J. Bowen. 1986. Shoaling surface gravity waves: a bispectral analysis, Proceedings of 20th Conf. on Coastal Engineering, Taipei, 150-162.
Doering J. C. and A. J. Bowen. 1995. Parametrization of orbital velocity asymmetries of shoaling and breaking waves using bispectral analysis, Coastal Eng., 26, 15-33.
Eldeberky Y. and J. Battjes. 1995. 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, 140-148.
Elgar S. and R. T. Guza. 1985. Observation of bispectra of shoaling surface gravity waves, J. Fluid Mech. 161, 425-448.
Elgar S. and R. T. Guza.1985. Shoaling gravity waves: comparison between field observations, linear theory and a nonlinear model, J. Fluid Mech. 158, 47-70.
Elgar S. and R. T. Guza. 1986. Nonlinear model predictions of bispectra of shoaling surface gravity waves, J. Fluid Mech. 167, 1-18.
Hasselmann K., W. Munk, and G. MacDonald. 1963. Bispectra of ocean waves, Proceedings of the Symp. on Time Series Analysis, 125-139.
Kim Y. and E. Powers. 1979. Digital bispectral analysis and its application to non-linear wave interaction, IEEE Trans. Plasma Sci. 1, 120-131.
Kuznetsov S. and Y. Saprykina. 2012. Secondary waves in coastal zone: physical mechanisms of formation and possible application for coastal protection. Proceeding of 33th International Conference on Coastal Engineering, dx.doi.org/10.9753/icce.v33.waves.12 .
Kuznetsov S.Yu., Ya.V. Saprykina, B.V. Divinskii, M.N. Shtremel, 2015. Spectral structure of breaking waves. Proceedings IMAM 2015, Towards Green Marine Technology and Transport, Taylor & Francis Group, London, 853-858.
Madsen P. A. and O. R. Sorensen. 1993. Bound waves and triad interactions in shallow water, J. Ocean Eng. 20 (4), 359-388.
Saprykina Ya. V., S. Yu. Kuznetsov, Zh. Cherneva, and N. Andreeva. 2009. Spatio-temporal variability of the amplitude-phase structure of storm waves in the coastal zone of the sea, Oceanology , 49 (2), 182-192.
Saprykina Ya. V., S. Yu. Kuznetsov, N. K. Andreeva, and M. N. Shtremel. 2013. Scenarios of nonlinear wave transformation in the coastal zone, Oceanology, 53 (4), 422-431.
Saprykina Ya.V., S.Yu.Kuznetsov, B.V.Divinskii. 2017. The influence of the processes of nonlinear transformations of waves in the coastal zone on the height of breaking waves, Oceanology, 57, in press.
Saprykina Y., B. Divinskiy, S. Kuznetsov. 2016. Relation of wave breaking criteria with spectral structures of waves. Proceedings of the 6th International Conference on the Application of Physical Modelling in Coastal and Port Engineering and Science (Coastlab16), Ottawa, Canada, http://rdio.rdc.uottawa.ca/publications/coastlab16/coastlab79.pdf
SWAN, Technical documentation, 2006. http://www.swan.tudelft.nl