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Laboratory investigations of deep-water wave transformation and stability

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EN
Abstrakty
EN
The authors performed laboratory investigations and the analysis of the transformation of deep-water waves in the flume of the Institute of Hydro-Engineering. Special wave trains were generated by our piston-type wavemaker. Due to the transformation the wave profiles changed along the path of propagation. At first, the changes appeared at the ends of the wave train. Far from the generator they intruded into the middle interval of initially regular waves. Finally, the whole wave train consisted of a set of irregular groups. To study the instability problem the wave trains were modulated by superposition of wave groups with very small amplitudes. The number of waves in a group was a very important parameter. When the number was proper, even small amplitudes of modulation resulted in strong development of amplitudes of wave groups. In our theoretical analysis the non-linear Schroedinger equation was used. The comparison of laboratory and theoretical results proved that this equation is useful but it does not describe the phenomenon in the best way. There have been many attempts to construct a numerical procedure that describes the propagation of water waves. Very often the numerical algorithm is not stable and the results of calculation diverge from the expected behaviour. The authors believe that in many cases the instability is due to the physical loss of stability of the wave train and thus it is necessary to have a good understanding of the physics of the studied motion.
Twórcy
autor
  • Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-953 Gdańsk, Poland
  • Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-953 Gdańsk, Poland
autor
  • Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-953 Gdańsk, Poland
autor
  • Institute of Hydro-Engineering of the Polish Academy of Sciences, ul. Kościerska 7, 80-953 Gdańsk, Poland
Bibliografia
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  • Benjamin T. B., Feir J. E. (1967), The Disintegration of Wavetrains on Deep Waters. Part 1. Theory, J. Fluid Mech., Vol. 27, 417-430.
  • Chereskin T. K., Mollo-Christensen E. (1985), Modulational Development of Non-linear GravityWave Groups, J. Fluid Mech., Vol. 151, 337-365.
  • Hasimoto H., Ono H. (1972), Non-linear Modulation of Gravity Waves, J. Phys. Soc. Jpn, Vol. 33, 805-811.
  • Hasselmann D. E. (1979), The High Wave Number Instabilities of a Stokes Wave, J. Fluid Mech., Vol. 93, 491-500.
  • Lake B. M., Yuen H. C. (1977), A Note on Some Non-linear Water Wave Experiments and the Comparison of Data with Theory, J. Fluid Mech., Vol. 83, 75-81.
  • Lake B. M., Yuen H. C., Rungaldier H., Ferguson W. (1977), Non-linear Deep-Water Waves: Theory and Experiment. Part 2. Evolution of a Continuous Wave Train, J. Fluid Mech., Vol. 83, 49-74.
  • Lighthill M. J. (1965), Contributions to the Theory of Waves in Non-linear Dispersive Systems, J. Inst. Math. Appl., Vol. 1, 269-306.
  • Pelinovsky E. N., Stiepanianc J. A., Filienkov S. E. (1988), Soliton Type Modulations in Dispersive Waves (in Russian), Internal report Department of Theoretical Physics, Gorki University.
  • Shemer L., Jiao Haying, Kit E. (1988), Experiments on Non-linear Wave Groups Shoaling in a Tank, Proc. of Coastal Engineering 1988, ASCE, Vol. 2, 645-655.
  • Skjelbreia L. (1959), Gravity Waves. Stokes' Third Oorder Approximation. Tables of Functions, Richmond Calif.; Council on Wave Research.
  • Sobierajski E. (1999), Testing of Wave Processes in the New Flume of the Institute of Hydro-Engineering, Internal report, (in Polish).
  • Stansberg C. T (1992), On Spectral Instabilities and Development of Non-linearities in Propagat¬ing Deep-water Wave Itains, Proc. of Coastal Engineering, 1992, ASCE, Vol. 1, 658-671.
  • Werhausen J. V., Laitone E. V. (1960), Surface Waves, [in] Encyclopedia of Physics, Springer Verlag, Berlin, Goettingen, Heidelberg.
  • Wilde P., Wilde M. (2001), On the Generation of Water Waves in a Flume, Archives of Hydro-Engineering and Environmental Mechanics, No. 4, 69-83.
  • Witham G. B.(1974), Linear and Non-linear Waves, Wiley, New York.
  • Yuen H. C., Lake B. M. (1982), Non-linear Dynamics of Deep Water Waves, Advances in Applied Mechanics, Vol. 22, 67-229.
  • Zacharov V. E, (1968), Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid, Sov. Phys. J. Appl. Mech. Tech. Phys., 4, 86-94.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT3-0021-0019
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