Evolutional Behaviour and Instability of a Single Wave Packet

  • Takao Yamashita
  • Yoshito Tsuchiya
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

Propagation of a single wave packet on a gently sloping bottom of 1/50 has been investigated experimentally over a wide range of maximum carrier wave steepness in order to elaborate on the wave packet instability. An instability diagram was derived as a function of wave steepness ak and the ratio of the water depth to the wave lengthness of maximum carrier wave kh (We will call it shallowness). Our conclusions indicate that even highly nonlinear carrier waves form an envelope propagating on a slope.

Keywords

Wave Packet Soliton Solution Slope Bottom Carrier Wave Wave Steepness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benjamin, T.B. and Feir, J.E.; The disintegration of water wavetrains on deep water. J. Fluid Mech., 27, 1967, pp.417–430.MATHCrossRefGoogle Scholar
  2. 2.
    Whitham, G.B.; Nonlinear dispersion of water waves. J. Fluid Mech., 27, 1967, pp. 399–412.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Lighthill, M.J.; Some special cases by the Whitham theory. Proc. Roy. Soc. London, Ser.A, 299, 1967, pp. 28–53.CrossRefGoogle Scholar
  4. 4.
    Benny, D.J. and Roskes, G.J.: Wave instabilities. Studies Appl. Math., 48, 1969, pp. 377–385.Google Scholar
  5. 5.
    Chu, V.C. and Mei, C.C.: The nonlinear evolution of Stokes waves in deep water. J. Fluid Mech., 47, 1971, pp. 337–352.MATHCrossRefGoogle Scholar
  6. 6.
    Davey, A and Stewartson, K.: On the three-dimensional packets of surface waves. Proc. Roy. Soc. London, Ser. A, 338, 1974, pp. 101–110.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Zakharov, V.E.: Exact theory of two-dimensional self-focusing and one-dimensional self modulation of waves in nonlinear media. Sov. Phys., JETP, 34, 1972, pp. 62–69.Google Scholar
  8. 8.
    Tsuchiya, Y.; Yasuda, T.; Yamashita, T. and Shibano, S.: Modulation and wavegrouping of nonlinear waves. Proc. 32nd Japanese Conf. Coas. Eng., 1985, pp. 179–183 (in Japanese).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Takao Yamashita
    • 1
  • Yoshito Tsuchiya
    • 1
  1. 1.Disaster Prevention Research InstituteKyoto UniversityUji, KyotoJapan

Personalised recommendations