Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T21:15:56.932Z Has data issue: false hasContentIssue false
  • English
  • Français

On slowly-varying Stokes waves

Published online by Cambridge University Press:  29 March 2006

Vincent H. Chu  and
Chiang C. Mei
Vincent H. Chu
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology
Chiang C. Mei
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

A WKB-perturbation technique is applied to study the slow modulation of a Stokes wave train on the surface of water. It is found that new terms directly representing modulation rates must be included to extend the scope of validity of Whitham's theory based on an averaged Lagrangian. Two examples are discussed. In the first, a monochromatic wave normally incident on a mild beach is studied and the local rate of depth variation is found to affect the wave phase. In the second, the ‘side-band instability’ problem of Benjamin & Feir is discussed from both linear and non-linear points of view.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 4 , 15 May 1970 , pp. 873 - 887
Copyright
© 1970 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

Battjes, J. A. 1968 J. Waterways Harb. Div., Proc. ASCE 94, 437.
Benjamin, T. B. 1967 Proc. Roy. Soc. A 299, 59.
Benjamin, T. B. & Feir, J. E. 1967 J. Fluid Mech. 27, 417.
Benney, D. J. & Newell, A. C. 1967 J. Math. & Phys. 46, 133.
Benney, D. J. & Rosenblat, S. 1964 Phys. Fluids, 7, 1385.
Benney, D. J. & Roskes, G. J. 1970 Studies in Appl. Math. (To be published.)
Bremmer, H. 1949 Physica, 15, 593.
Bretherton, F. P. 1968 Proc. Roy. Soc. A 302, 555.
Eagleson, P. S. 1956 Trans. Amer. Geophys. Union, 37, 565.
Feir, J. E. 1967 Proc. Roy. Soc. A 299, 54.
Galvin, C. J. 1968 Trans. Amer. Geophys. Union, 44, 206.
Gardner, C. S., Greene, J. M. Kruskal, M. D. & Miura, R. M. 1967 Phys. Rev. Lett. 19, 1095.
Hoogstraten, H. W. 1968 J. Eng. Math. 2, 249.
Hoogstraten, H. W. 1969 J. Eng. Math. 3, 45.
Kajiura, K. 1961 I.U.G.G. Monograph, 24, 206.
Longuet-Higgins, M. S. & Stewart, R. W. 1962 J. Fluid Mech. 13, 481.
Luke, J. C. 1966 Proc. Roy. Soc. A 292, 403.
Madsen, O. S. & Mei, C. C. 1969a J. Fluid Mech. 39, 781.
Madsen, O. S. & Mei, C. C. 1969b Hydrodynamics Laboratory, M.I.T. Tech. Rep. 117.
Mei, C. C., Tlapa, G. A. & Eagleson, P. S. 1968 J. Geophys. Res. 73, 4555.
Street, R. L., Burges, S. J. & Whitford, P. W. 1968 Department of Civil Engineering, Stanford University, Tech. Rep. 93.
Whitham, G. B. 1962 J. Fluid Mech. 12, 135.
Whitham, G. B. 1965a J. Fluid Mech. 22, 273.
Whitham, G. B. 1965b Proc. Roy. Soc. A 283, 238.
Whitham, G. B. 1967a J. Fluid Mech. 27, 399.
Whitham, G. B. 1967b Proc. Roy. Soc. A 299, 6.
Zabusky, N. J. & Kruskal, M. D. 1965 Phys. Rev. Lett. 15, 240.