Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T19:53:40.016Z Has data issue: false hasContentIssue false
  • English
  • Français

Long waves induced by short-wave groups over an uneven bottom

Published online by Cambridge University Press:  20 April 2006

Chiang C. Mei  and
Chakib Benmoussa
Chiang C. Mei
Affiliation:
Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology
Chakib Benmoussa
Affiliation:
Parsons Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 219 - 235
Copyright
© 1984 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

Benmoussa, C. 1983 Wave-current interaction over uneven topography. M.S. thesis, Department of Civil Engineering, Massachusetts Institute of Technology.
Bowen, A. J. 1969 The generation of longshore currents on a plane beach J. Mar. Res. 27, 206–214.Google Scholar
Bowers, E. C. 1977 Harbour resonance due to set-down beneath wave groups J. Fluid Mech. 79, 71–92.Google Scholar
Burnside, W. 1915 On the modulation of a train of waves as it advances into shallow water Proc. Lond. Math. Soc. 14, 131–133.Google Scholar
Chen, H. S. & Mei, C. C. 1974 Oscillations and wave forces in an offshore harbor in the open sea. Proc. 10th Symp. Naval Hydrodyn., pp. 573–594.Google Scholar
Chu, V. H. & Mei, C. C. 1970 On slowly varying Stokes waves J. Fluid Mech. 41, 873.Google Scholar
Foda, M. A. & Mei, C. C. 1981 Nonlinear excitation of long trapped waves by a group of short swells J. Fluid Mech. 111, 319–345.Google Scholar
Hansen, N.-E. O. 1978 Long period waves in natural wave trains. Prog. Rep. no. 46, Tech. Univ. Denmark, Inst. Hydrodyn. and Hydraul. Engng, pp. 13–24.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy around islands J. Fluid Mech. 29, 781–821.Google Scholar
Longuet-Higgins, M. S. 1970a Longshore currents generated by obliquely incident sea waves. Part 1 J. Geophy. Res. 75, 6778–6789.Google Scholar
Longuet-Higgins, M. S. 1970b Longshore currents generated by obliquely incident sea waves. Part 2 J. Geophys. Res. 75, 6790–6801.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in the form of short gravity waves on long waves and tidal current J. Fluid Mech. 8, 565–583.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents J. Fluid Mech. 10, 529–549.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1962 Radiation stress and mass transport in gravity waves, with application to ‘surf-beats’. J. Fluid Mech. 13, 481–481.Google Scholar
Mei, C. C. 1982 The Applied Dynamics of Ocean Surface Waves. Wiley Interscience.
Molin, B. 1982 On the generation of long-period second order free waves due to changes in the bottom profile. Rapp. IFP: 30167, Inst. Français du Petrole. [Also published as Ship Res. Inst. Rep. 68, Tokyo, Japan.]Google Scholar
Sand, S. E. 1982 Long wave problems in laboratory models J. Waterways, Port, Coastal & Ocean Div. ASCE 108(WW4), 492–492.Google Scholar
Thornton, E. B. 1970 Variation of longshore current across the surface zone. In Proc. 12th Coastal Engng. Conf. pp. 291–308. ASCE.