Skip to main content
×
Home
    • Aa
    • Aa

Long wavelength bifurcation of gravity waves on deep water

  • P. G. Saffman (a1)
Abstract

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of determining the stability of the new waves.

Copyright
References
Hide All
Chen, B. & Saffman, P. G. 1980 Numerical evidence for the existence of new types of gravity wave of permanent form on deep water. Stud. Appl. Math. 62, 121.
Cokelet, E. D. 1974 Steep gravity waves in water of arbitrary uniform depth. Phil. Trans. Roy. Soc. A. 286, 183230.
Garabedian, P. B. 1965 Surface waves of finite depth. J. D’ Analyse Math. 14, 161169.
Keller, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. Applications of Bifurcation Theory, pp. 359384. Academic.
Lighthill, M. J. 1967 Some special cases treated by the Whitham theory. Proc. Roy. Soc. A 299, 2853.
Longuet-Higgins, M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. Soc. A 342, 157174.
Longuet-Higgins, M. S. 1978a Some new relations between Stokes’ coefficients in the theory of gravity waves. J. Inst. Math. Applies. 22, 261273.
Longuet-Higgins, M. S. 1978b The instabilities of gravity waves of finite amplitude in deep water. II. Subharmonics. Proc. Roy. Soc. A 360, 489505.
Peregrine, D. H. & Thomas, G. P. 1979 Finite amplitude deep water waves on currents. Phil. Trans. Roy. A 292, 371390.
Saffman, P. G. & Szeto, R. 1980 Structure of a linear array of uniform vortices. Stud. Appl. Math. (to appear).
Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes expansion for gravity waves. J. Fluid Mech. 62, 553578.
Stokes, G. G. 1880 Supplement to a paper on the theory of oscillatory waves. Mathematical and Physical Papers, vol. 1, pp. 225228. Cambridge University Press.
Whitham, G. B. 1965 A general approach to linear and nonlinear dispersive waves using a Lagrangian. J. Fluid Mech. 22, 273283.
Whitham, G. B. 1970 Two-timing, variational principles and waves. J. Fluid Mech. 44, 373395.
Whitham, G. B. 1974 Linear and Non-linear waves. Wiley-Interscience.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 66 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd October 2017. This data will be updated every 24 hours.