Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-07-05T23:58:19.883Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of nonlinearity and spectral bandwidth on the dispersion relation and component phase speeds of surface gravity waves

Published online by Cambridge University Press:  20 April 2006

Donald R. Crawford ,
Bruce M. Lake ,
 and
Henry C. Yuen
Donald R. Crawford
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Bruce M. Lake
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Henry C. Yuen
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, One Space Park, Redondo Beach, California 90278
Get access Rights & Permissions [Opens in a new window]

Abstract

The dispersion relation and component phase speeds of surface gravity wavefields and modulated wavetrains are calculated. A parametric study is performed for a range of nonlinearity and spectral bandwidths. It is found that the amount of departure from linear theory increases with the ratio of nonlinearity to spectral bandwidth. The calculated results are compared quantitatively with laboratory and ocean measurements of wavetrains and wavefields with and without wind. The good agreement between theory and experiment suggests that the nonlinearity–dispersion balance is a likely candidate to account for the observed discrepancy between linear theory and data, as well as for the difference in behaviour between laboratory and oceanic wave measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 1 - 32
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains in deep water. Part 1. Theory. J. Fluid Mech. 27, 417–430.Google Scholar
Crawford, D. R., Lake, B. M., Saffman, P. G. & Yuen, H. C. 1981 Stability of weakly nonlinear deep-water waves in two and three dimensions. J. Fluid Mech. 105, 177–191.Google Scholar
Crawford, D. R., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion 2, 1–16.Google Scholar
Grose, P. L., Warsh, K. L. & Garstang, M. 1972 Dispersion relations and wave shapes. J. Geophys. Res. 77, 3902–3906.Google Scholar
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–500.Google Scholar
Hasselmann, K. 1963 On the nonlinear energy transfer in a gravity-wave spectrum, 2. Conservation theorems, wave—particle correspondence, irreversibility. J. Fluid Mech. 15, 273–281.Google Scholar
Huang, N. E. & Tung, C. C. 1977 The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field. J. Phys. Oceanog. 7, 403–414.Google Scholar
Lake, B. M. & Yuen, H. C. 1978 A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence. J. Fluid Mech. 88, 33–62.Google Scholar
Masuda, A., Kuo, Y. Y. & Mitsuyasu, H. 1979 On the dispersion relation of random gravity waves. Part 1. Theoretical framework. J. Fluid Mech. 92, 717–730.Google Scholar
Mitsuyasu, H., Kuo, Y. Y. & Masuda, A. 1979 On the dispersion relation of random gravity waves. Part 2. An experiment. J. Fluid Mech. 92, 731–749.Google Scholar
Mollo-Christensen, E. & Ramamonjiarisoa, A. 1978 Modeling the presence of wave groups in a random wave field. J. Geophys. Res. C 83, 4117–4122.Google Scholar
Plant, W. J. & Wright, J. W. 1979 Spectral decomposition of short gravity wave systems. J. Phys. Oceanog. 9, 621–624.Google Scholar
Ramamonjiarisoa, A. 1974 Thèse de Doctorat d'Etat, Université de Provence, enregistrée au C.N.R.S. no. A.0.10.023.
Ramamonjiarisoa, A. & Coantic, M. 1976 Loi expérimental de dispersion des vagues produites parle vent sur une faible longueur d'action. C. R. Acad. Sci. Paris B 282, 111–113.Google Scholar
Ramamonjiarisoa, A. & Giovanangeli, J. P. 1978 Observations de la vitesse de propagation des vagues engendrées par le vent au large. C. R. Acad. Sci. Paris B 287, 133–136.Google Scholar
Rikiishi, K. 1978 A new method for measuring the directional wave spectrum. Part II. Measurement of the directional spectrum and phase velocity of laboratory wind waves. J. Phys. Oceanog. 8, 518–529.Google Scholar
Saffman, P. G. & Yuen, H. C. 1978 Nonlinear deep-water waves. VII. Multiple time scales approach to nonlinear interactions in a gravity wave field. TRW Rep. no. 31326–6038-RU-00.Google Scholar
Von Zweck, O. H. 1970 Observations of propagation characteristics of a wind driven sea. Doctorate thesis, Massachusetts Institute of Technology.
Yefimov, V. V., Solov'yev, Y. P. & Khristoforov, G. N. 1972 Observational determination of the phase velocities of spectral components of wind waves. Atmospheric & Ocean Phys. 8, 435–446.Google Scholar
Yuen, H. C. & Lake, B. M. 1978 A new model for nonlinear wind waves. Part 2. Theoretical model. Stud. Appl. Math. 60, 261–270.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 86–94.Google Scholar