DOI QR코드

DOI QR Code

Laboratory study on the modulation evolution of nonlinear wave trains

  • Dong, G.H. (State Key Laboratory Of Coastal And Offshore Engineering, Dalian University Of Technology) ;
  • Ma, Y.X. (State Key Laboratory Of Coastal And Offshore Engineering, Dalian University Of Technology) ;
  • Zhang, W. (State Key Laboratory Of Coastal And Offshore Engineering, Dalian University Of Technology) ;
  • Ma, X.Z. (State Key Laboratory Of Coastal And Offshore Engineering, Dalian University Of Technology)
  • 투고 : 2012.03.26
  • 심사 : 2012.07.31
  • 발행 : 2012.09.25

초록

New experiments focusing on the evolution characteristics of nonlinear wave trains were conducted in a large wave flume. A series of wave trains with added sidebands, varying initial steepness, perturbed amplitudes and frequencies, were physically generated in a long wave flume. The experimental results show that the increasing wave steepness, increases the speed of sidebands growth. To study the frequency and phase modulation, the Morlet wavelet transform is adopted to extract the instantaneous frequency of wave trains and the phase functions of each wave component. From the instantaneous frequency, there are local frequency downshifts, even an effective frequency downshift was not observed. The frequency modulation increases with an increase in amplitude modulation, and abrupt changes of instantaneous frequencies occur at the peak modulation. The wrapped phase functions show that in the early stage of the modulation, the phase of the upper sideband first diverges from that of the carrier waves. However, at the later stage, the discrepancy phase from the carrier wave transformed to the lower sideband. The phase deviations appear in the front of the envelope's peaks. Furthermore, the evolution of the instantaneous frequency exhibits an approximate recurrence-type for the experiment with large imposed sidebands, even when the corresponding recurrence is not observed in the Fourier spectrum.

키워드

참고문헌

  1. Banner, M.L. and Peirson, W.L. (2007), "Wave breaking onset and strength for two-dimensional deep-water wave groups", J. Fluid Mech., 585, 93-115. https://doi.org/10.1017/S0022112007006568
  2. Banner, M.L. and Tian, X. (1998), "On the determination of the onset of breaking for modulating surface gravity waves", J. Fluid Mech., 367, 107-137. https://doi.org/10.1017/S0022112098001517
  3. Benjamin, T.B. (1967), "Instability of periodic wavetrains in nonlinear dispersive systems", Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences.
  4. Benjamin, T.B. and Feir, J.E. (1967), "The disintegration of wave trains on deep water", J. Fluid Mech., 27(3), 417-430. https://doi.org/10.1017/S002211206700045X
  5. Dysthe, K. (1979), "Note on a modification to the nonlinear Schrödinger equation for application to deep water waves", Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences.
  6. Farge, M. (1992), "Wavelet transforms and their applications to turbulence", Annu. Rev. Fluid Mech., 24, 395-457. https://doi.org/10.1146/annurev.fl.24.010192.002143
  7. Hammack, J.L. and Henderson, D.M. (1993), "Resonant interactions among surface-water waves", Annu. Rev. Fluid Mech., 25, 55-97. https://doi.org/10.1146/annurev.fl.25.010193.000415
  8. Hwung, H.H., Chiang, W.S. and Hsiao, S.C. (2007), "Observations on the evolution of wave modulation", Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences.
  9. Kharif, C., Kraenkel, R.A., Manna, M.A. and Thomas, R. (2010), "The modulational instability in deep water under the action of wind and dissipation", J. Fluid Mech., 664, 138-149. https://doi.org/10.1017/S0022112010004349
  10. Lake, B.M., Yuen, H.C., Rungaldier, H. and Ferguson, W.E. (1977), "Nonlinear deep-water waves - theory and experiment .2. evolution of a continuous wave train", J. Fluid Mech., 83, 49-74. https://doi.org/10.1017/S0022112077001037
  11. Lo, E. and Mei, C.C. (1985), "A numerical study of water-wave modulation based on a higher-order nonlinear schrodinger-equation", J. Fluid Mech., 150, 395-416. https://doi.org/10.1017/S0022112085000180
  12. Longuet-Higgins, M.S. (1980), "Modulation of the amplitude of steep wind-waves", J. Fluid Mech., 99, 705-713. https://doi.org/10.1017/S0022112080000845
  13. Ma, Y., Dong, G., Perlin, M., Ma, X., Wang, G. and Xu, J. (2010), "Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents", J. Fluid Mech., 661, 108-129. https://doi.org/10.1017/S0022112010002880
  14. Massel, S.R. (2001), "Wavelet analysis for processing of ocean surface wave records", Ocean Eng., 28(8), 957-987. https://doi.org/10.1016/S0029-8018(00)00044-5
  15. Melville, W.K. (1982), "The instability and breaking of deep-water waves", J. Fluid Mech., 115, 165-185. https://doi.org/10.1017/S0022112082000706
  16. Melville, W.K. (1983), "Wave modulation and breakdown", J. Fluid Mech., 128, 489-506. https://doi.org/10.1017/S0022112083000579
  17. Segur, H., Henderson, E., Carter, J., Hammack, J., Li, C.M., Pheiff, D. and Socha, K. (2005), "Stabilizing the benjamin-feir instability", J. Fluid Mech., 539, 229-271. https://doi.org/10.1017/S002211200500563X
  18. Su, M.Y. (1982), "Three-dimensional deep-water waves. Part 1. Experimental measurements of skew and symmetric wave patterns", J. Fluid Mech., 124, 73-108. https://doi.org/10.1017/S0022112082002419
  19. Tian, Z., Perlin, M. and Choi, W. (2008), "Evaluation of a deep-water breaking criterion", Phys. Fluids., 20, 066604. https://doi.org/10.1063/1.2939396
  20. Tian, Z., Perlin, M. and Choi, W. (2010), "Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model", J. Fluid Mech., 655, 217-257. https://doi.org/10.1017/S0022112010000832
  21. Trulsen, K. and Dysthe, K.B. (1996), "A modified nonlinear schrodinger equation for broader bandwidth gravity waves on deep water", Wave Motion, 24(3), 281-289. https://doi.org/10.1016/S0165-2125(96)00020-0
  22. Tulin, M.P. and Waseda, T. (1999), "Laboratory observations of wave group evolution, including breaking effects", J. Fluid Mech., 378, 197-232. https://doi.org/10.1017/S0022112098003255
  23. Waseda, T. and Tulin, M.P. (1999), "Experimental study of the stability of deep-water wave trains including wind effects", J. Fluid Mech., 401, 55-84. https://doi.org/10.1017/S0022112099006527
  24. Zakharov, V.E. (1968), "Stability of periodic waves of finite amplitude on the surface of deep fluid", J. Appl. Mech. Tech. Phys., 9(2), 190-194.

피인용 문헌

  1. An experimental and numerical study on breather solutions for surface waves in the intermediate water depth vol.133, 2017, https://doi.org/10.1016/j.oceaneng.2017.01.030
  2. Boussinesq equations for internal waves in a two-fluid system with a rigid lid vol.6, pp.1, 2016, https://doi.org/10.12989/ose.2016.6.1.117