Keywords
giant wave
phase speed
nonlinear wave
How to Cite
Abstract
Wave modulation due to Bengamin Feir Instability (BFI) in the presence of long wave (swell) is investigated in the elaborate experiments. The mechanically generated waves are composed of three discrete waves; while the newly generated harmonics due to BFI still combining into discrete spectra with the same frequency difference step. These stable discrete waves allow us to further examine the basic properties of nonlinear wave-wave interactions, such as the variation of phase speeds and wave numbers along the wave tank together with speed of crests, especial for the large transient waves. The measured values have a reasonable correspondence to the available nonlinear model estimations. The technique proposed in this study is verified to accurately measure the phase speed and wave number of each harmonic in the wave group. Phase speeds of short waves have a significant amplification in the vicinity of big transient waves, while the speeds of longer waves are close to linear values. The relative long wave (storm wave) travelling with short waves (wind waves) dramatically change the local kurtosis and skewness and may have an important role for the generation of large transient wave and provide an opportunity for triggering the freak waves.References
Benjamin, T. B. and J. E. Feir 1967. 'Disintegration of wave Trains on deep Water .1. Theory', Journal of Fluid Mechanics 27: 417
Banner, M. L., Barthelemy X., Fedele F., Allis M., Benetazzo A., Dias F. and Peirson, W. L. 2014. 'Linking Reduced Breaking Crest Speeds to Unsteady Nonlinear Water Wave Group Behavior', Phys. Rev. Lett., 112 114502.
Chiang, W.-S. and H.-H. Hwung 2007. 'Steepness effect on modulation instability of the nonlinear wave train.' Physics of Fluids 19(1).
Grue, J., Clamond, D., Huseby, M., and Jensen, A., 2003 'Kinematics of extreme waves in deep water.' Applied Ocean Research 25(6): 355-366.
Galchenko A., Babanin A. V., Chalikov D., Young I.R., and Hsu T.W., 2010 'Modulational Instabilities and Breaking Strength for Deep-Water Wave Groups.' J. Phys. Oceanogr., 40, 2313-2324.
Hwung, H. H., W. S. Chiang and S.C. Hsiao 2007. 'Observations on the evolution of wave modulation.' Proceedings of the Royal Society, 463(2077): 85-112.
Hwung, H.-H., Chiang W.-S., Yang, R.-Y. and Shugan, I. V. 2011 'Threshold Model on the Evolution of Stokes Wave Side-Band Instability.' Eur. J. Mech. B/Fluids, 30 147-155.
Janssen, P. 2003. 'Nonlinear four-wave interactions and freak waves.' Journal of Physical Oceanography, 33(4): 863-884.
Kharif, C. and E. Pelinovsky 2003. 'Physical mechanisms of the rogue wave phenomenon.' European Journal of Mechanics B-Fluids 22(6): 603-634.
Kartashova E., Shugan I. 2011. 'Dynamical cascade generation as a basic mechanism of Benjamin-Feir instability'. Europian Physics Letters. V.95, 30003.
Lake, B . M., Yuen,H . C., Rungaldiehr, and Ferqusown E. 1977 'Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train' Journal of Fluid Mechanics 83: 49-74
Longuet-Higgins MS 1975 'Integral properties of periodic gravity waves of finite amplitudes.' Proc R Soc London ,342:157-74.
Melville, W. K. 1983. 'Wave modulation and breakdown.' Journal of Fluid Mechanics 128: 489-506.
Phillips, O . M . 1977. The Dynamics of the Upper Ocean. Cambridge: Cambridge
Stansell P. and MacFarlane C., 2002 'Experimental Investigation of Wave Breaking Criteria Based on Wave Phase Speeds.' J. Phys. Oceanogr., 32, 1269-1283.
Tulin, M. P. and T. Waseda 1999. 'Laboratory observations of wave group evolution, including breaking effects.' Journal of Fluid Mechanics 378: 197-232.
Tamura, H., T. Waseda, and Y. Miyazawa 2009, 'Freakish sea state and swell-windsea coupling: Numerical study of the Suwa-Maru incident,' Geophys. Res. Lett., 36, L01607