Hostname: page-component-84b7d79bbc-rnpqb Total loading time: 0 Render date: 2024-07-28T08:21:52.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Resonant interactions among capillary-gravity waves

Published online by Cambridge University Press:  28 March 2006

Lawrence F. Mcgoldrick
Lawrence F. Mcgoldrick
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
Get access Rights & Permissions [Opens in a new window]

Abstract

The analysis presented here is a second-order analysis of the resonant interactions triads of waves with wavelengths in the capillary-gravity and pure capillary ranges. The analysis is not a power series perturbation analysis, and one of the objects is the removal of the secularity which arises through power series perturbations. It is further found that the interactions are energy-conserving to the order considered here. Suitable modifications are made to accommodate the inevitable viscous attenuation associated with these small wavelengths. A start is made toward describing more completely the various spectra of random seas in wave-number and frequency regions where these interactions are dynamically significant.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 2 , February 1965 , pp. 305 - 331
Copyright
© 1965 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

Benney, D. J. 1962 Non-linear gravity wave interactions. J. Fluid Mech. 14, 577–84.Google Scholar
Bogoliubov, N. N. & Mitropolski, Ya. A. 1961 Asymptotic Methods in the Theory of Non-linear Oscillations. Delhi: Hindustan Publishing Corp.
Brooke Benjamin, T. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. A, 245, 535–81.Google Scholar
Longuet-Higgins, M. S. 1962 Resonant interactions between two trains of gravity waves. J. Fluid Mech. 12, 321–32.Google Scholar
Miles, J. W. 1962 On the generation of surface waves by shear flows, Part 4. J. Fluid Mech. 13, 433–48.Google Scholar
Milne-Thomson, L. M. 1950 Jacobian Elliptic Function Tables. New York: Dover Publications, Inc.
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–45.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude, Part 1, The elementary interactions. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. 1961 A note on the turbulence generated by gravity waves. J. Geophys. Res. 66 (9), 2889–93.Google Scholar
Pierson, W. J. 1961 Comments on a paper by O. M. Phillips, appearing in Proceedings of a Conference on Ocean Wave Spectra, Easton, Md., 1961. Published as Ocean Wave Spectra, pp. 180–6 and 187–8. Prentice-Hall, Inc., Englewood Cliffs, N. J. (1963).
Pierson, W. J. & Fife, P. 1961 Some non-linear properties of long crested periodic waves with lengths near 2.44 centimeters. J. Geophys. Res. 66, (1), 163–79.Google Scholar
Tick, L. J. 1961 Comments on a paper by O. M. Phillips, appearing in Proceedings of a Conference on Ocean Wave Spectra, Easton, Md., 1961. Published as Ocean Wave Spectra, pp. 179–80. Prentice-Hall, Inc., Englewood Cliffs, N. J. (1963).
Wilton, J. R. 1915 On ripples. Phil. Mag. (6) 29, 173.Google Scholar